Electricity and Magnetism

[Janus]

Need help with this topic which includes elective forces, electric fields and electrical energy and capacitance.

Additional questions:
The book states that electric charge is always conserved so is this similar to the conservation of energy in any way?

I don't understand the difference between potential difference and a difference in potential energy. I also need help with problems concerning resultant forces in conjunction with Coulomb's Law and the superposition principle.

[ComradeRed]

The book states that electric charge is always conserved so is this similar to the conservation of energy in any way? Sort of, if we have a system of charged particles, and the charge is exchanged within the system, the total charge of the system remains the same (provided it is a closed system of course :)).

Electricity and magnetism...hmmm...do you know calculus? Because the easiest way that I learnt electromagnetism was through something called Maxwell's equations (http://en.wikipedia.org/wiki/Maxwell%27s_equations).

They are four simple equations that beautifully unify electromagnetism.

Potential difference is the amount of energy it would take to move a charged object some distance.

A difference in potential is potential at time t_0 (q_0) compared to a later measure of its charge at t_1 (q_1); the difference in potential in this example q_1 - q_0.

The electric field is in maxwell's equations, if I recall correctly it is div E = rho, where E is the electric force vector and rho is the potential density.

Hope this helps some ;) I'll probably be of more use later...

[edit]
I forgot the superposition principle. Well, think of a positive charge as a vector. It is mapped on a number line. Depending on how long it is, that indicates how large of a charge it is.

A positive charge points to the positiv direction, and a negative charge in the negative direction.

The superposition principle is easy: if a system has more than one charge, add up the vectors for the components, and the sum is equal to the charge of the system.

Or if you don't want to do all that geometry, just add up the charges of the components and this is the charge of the system. :)

Capacitance can be thought of as the flux of the charge over the potential energy. It "stores" a charge, if I remember correctly. Yep total charge per total energy (in units of farads per volts).

[Janus]

do you know calculus
No. Will it help with physics besides allowing you to derive equations?

I don't really understand this whole charge thing.

[ComradeRed]

No. Will it help with physics besides allowing you to derive equations? It helps a lot with AP physics.

It helps overall too. There's only two things you need to know that's fairly straightforward, derivatives and integrals. Just learn them algebraically (e.g. the derivative of f(x) = x^n is n*x^{n-1}), then you'll be fine ;)

It doesn't really matter one way or the other.



I don't really understand this whole charge thing. What about it specifically?

It's an inherent part of a system, at least in physics ;)

[Janus]

What about it specifically?
Nothing specific. I'm not really sure what it's supposed to denote or what the purpose for it is.


So for vectors, all I have to do is
1. Find the x component of the force.
2. Find the y component of the force.
3. Then add x^2 to Y^2 and find the square root of that answer.
This is all I have to do in order to find the resultant forcefor charges and in their electric fields?
But in order to find the electric potential, I just simply add the potentials right? How come?

Also, Why do the electric field vector due to a point charge, force(from Coulomb's Law), electric potential, and potential energy all have the same equation?

[ComradeRed]

Nothing specific. I'm not really sure what it's supposed to denote or what the purpose for it is.
Well, the electric charge -- if you want to get the "nitty-gritty details" -- has to do with the spin of the electron. If you're bored, look into what P.A.M. Dirac did with pioneering early attempts at Quantum Electrodynamics (QED).

It's fascinating stuff.



So for vectors, all I have to do is
1. Find the x component of the force.
2. Find the y component of the force.
3. Then add x^2 to Y^2 and find the square root of that answer.
This is all I have to do in order to find the resultant forcefor charges and in their electric fields?
But in order to find the electric potential, I just simply add the potentials right? How come? Well if you are working in two dimensions, yes. But if you are working in three dimensions, you would have to include the z component.

It essentially is the squareroot of the dot product of the force vector with itself.

The reason is that regardless of whether the is negative or positive in one spatial dimension, it still acts.

Plus mathematically, it gives the generalized force in every direction; with potentials, to do the same thing, you only need addition or subtraction.

Potentials are irrelevant to orientation. Potential depends solely on the force.

Mathematically, the potential is such that the divergence is equal to the field (ie force).

[Janus]

Okay, so here are some of the problems from the electric forces and electric fields chapter.

7. The Moon and Earth are bound together by gravity. If, instead, the force of attraction were the result of each having a charge of the same magnitude but opposite in sign, find the quantity of charge that would have to be placed on each to produce the required force.

24. An electron and a proton both start from rest and from the same point in a uniform electric field of 370 N/C. How far apart are they after 1.0 microseconds after they are released? Ignore the attraction between the elctron and proton. (Hint: Imagine the experiment performed with the proton only, and then repeat with the electron only).

That's all for now.

Edit: No clue on this problem

11. A molecule of DNA is 2.17 micrometers long. The ends of the molecule become simply ionized-negative on one end, positive on the other. The helical molecule acts as a spring and compresses 1.00% upon becoming charged. Determine the effective spring constant of the molecule

[Janus]

Also, I'm not so sure about this problem

2. A typical lead-acid storage battery contains sulfuric acid, H2SO4, which breaks down into 2H+SO4 and each molecule delivers two electrons to the external circuit. If the battery delivers a total charge of 2.0 times 10^5, how many grams of sulfuric acid are used up?

Am I suppose to add the electrons' charges together and then find the amount of grams?

[Janus]

Here's another problem that I'm not too sure about.

10. Calculate the magnitude and direction of the Coulomb force on each of the three charges.
Since I can't scan the diagram, I'll attempt to describe it.
Charge 1 has a charge of 6 micro Coulombs and is 3 cm from Charge 2. Charge 2 has a charge of 1.5 micro Coulombs and is a distance of 2 cm from Charge 3. Charge 3 has a charge of -2 micro Coulombs.
So, do each of the charges exert a force on each other? For example, do both Charge 1 and Charge 2 exert a force on Charge 3. Also, how do I calculate the direction of the charge?

[Janus]

29. A piece of aluminum foil of mass 5.00 times 10^-2 kg is suspended by a string in an electric field directed vertically upward. If the charge on the foil is 3.00 micro Coulombs, find the strength of the field that will reduce the tension in the string to zero.

I don't understand how to place tension into this problem. :(

33. A proton accelerates from rest in a uniform electric field of 640 N/C. At some time later, its speed is 1.20 times 10^6. (a) Find the magnitude of the acceleration of the proton. (b) How long does it take the proton to reach this speed? © How far has it moved in this interval? (d) What is its kinetic energy at the later time?

Come on, there has to other comrades here who understand physics besides ComradeRed. Right?

[ComradeRed]

29. A piece of aluminum foil of mass 5.00 times 10^-2 kg is suspended by a string in an electric field directed vertically upward. If the charge on the foil is 3.00 micro Coulombs, find the strength of the field that will reduce the tension in the string to zero. Well, remember that tension is of the units joules per cubic meter, or Newtons per square meter (they're equivalent ;)).

Now, the tension acting on the string would be caused by gravity (attracted to the Earth with an acceleration of 9.832 meters per second squared). We only really need to be working within the frame of one second, so (5*10^-2 kg)(1 sec)(9.832 m/sec^2) = 0.4916 Newton.

Cancel this out with the energy from the electric field, which is ((3.00 * 10^-3 C)(? C)/m^2) 8.988 * 10^9 Nm^2/C^2 = 0.4916 N. Note that 8.988*10^9 Nm^2/C^2 is a constant.

It turns out that ? C = 0.4916 N/(8.988*10^9 N/C^2)(3.00*10^-3 C) = 1.82317163625574840528111556148939 * 10^-8 C. The field strength must be 0.4916 N in order to counteract string tension.



33. A proton accelerates from rest in a uniform electric field of 640 N/C. At some time later, its speed is 1.20 times 10^6. (a) Find the magnitude of the acceleration of the proton. (b) How long does it take the proton to reach this speed? © How far has it moved in this interval? (d) What is its kinetic energy at the later time?
(a) Well, the magnitude of the acceleration is given by a = v^2 / r. Through some algebra, we get a*r = v^2, thus v^2 = 1.44 * 10^12; remember that the distance in terms of acceleration is a conic.

I actually did this backwards and found b and c first, then found out that the solution here is 6.13053318244649049384192575736966 * 10^11.

(b)Remember that the proton has a fundamental charge of +1 ("+e"). This is +1.60217653(14) * 10^-19 C; thus according to algebra the force acting on it is 1025.392980096 * 10^-19 N. The mass of a proton is 1.6726 * 10^−27 kg; therefore the acceleration is 613.053318244649049384192275499223 * 10^9 meters per second squared.

The velocity per acceleration gives us the time it took. That is, it took was 1.95741538996306384169271947931375 * 10^-6 sec.
0.00000195741538996306384169271947931375

© It has traveled 2.3488984679556766100312622248235 meters.

(d) The kinetic Energy is (1025.392980096 * 10^-19 N)(2.3488984679556766100312622248235 meters) = 2.40854399999999999999999882043569 * 10^-16 joules.

[ComradeRed]

7. The Moon and Earth are bound together by gravity. If, instead, the force of attraction were the result of each having a charge of the same magnitude but opposite in sign, find the quantity of charge that would have to be placed on each to produce the required force. The moon weighs 7.347673*10^22 kg, and the earth weighs 5.9736*10^24 kilograms, thus

(2/3 * 10^-10 meters^3/(kilograms*sec^2))(7.347673*10^22 kg * 5.9736*10^24 kg)/(384000 km)^2 = 1.9844138560112847222222222222222*10^20 N. Remember that the radius is in km, not m.

Now the force that would be equivalent to that with the same magnitude? That means the ratio of the charge of the earth to the charge of the moon has to be equal to the mass of the earth to the mass of the moon. That is 1.23002427346993437792955671621803 * 10^-2.

Now, the lazy way to do this is to figure out the ratio of the constants (2/3)(10^-10) compared to coulomb's constant (8.988 * 10^9), that is 5.39280000000000000000000000012634.

Place the first ratio over the second to get 0.00228086388048867819672444132207992. Multiply the masses by this to get the charge, with the magnitude integrated into it ;)


24. An electron and a proton both start from rest and from the same point in a uniform electric field of 370 N/C. How far apart are they after 1.0 microseconds after they are released? Ignore the attraction between the elctron and proton. (Hint: Imagine the experiment performed with the proton only, and then repeat with the electron only).

That's all for now. Basically do the same thing I did for the othe one, but double the distance


11. A molecule of DNA is 2.17 micrometers long. The ends of the molecule become simply ionized-negative on one end, positive on the other. The helical molecule acts as a spring and compresses 1.00% upon becoming charged. Determine the effective spring constant of the molecule Well, remember Hooke's Law F = − kx, where this time x=-.217 micrometers.

We can determine that the force is equal to the distance per time squared, coupled to the mass. Alternatively we can use coulomb's law to deduce that based on the information that there are charges present, thus there is a force.

The charges are elementary charges, naturalement, thus the force becomes (8.988*10^9)((+and-1.60217653 * 10^-19)^2 / (2.17 * 10^-4 meters)^2) = -4.89964175581264711699122937416079 * 10^9 N. This per distance is equal to the constant being 22.5789942664177286497291676228608 * 10^4 meters kilograms per second.

Easy as a piece of pi :redstar2000:

[Janus]

It turns out that ? C = 0.4916 N/(8.988*10^9 N/C^2)(3.00*10^-3 C) = 1.82317163625574840528111556148939 * 10^-8 C. The field strength must be 0.4916 N in order to counteract string tension.

For number 29, the book gives an answer of 1.63 times 10^5 N/C.


I actually did this backwards and found b and c first, then found out that the solution here is 6.13053318244649049384192575736966 * 10^11.

(b)Remember that the proton has a fundamental charge of +1 ("+e"). This is +1.60217653(14) * 10^-19 C; thus according to algebra the force acting on it is 1025.392980096 * 10^-19 N. The mass of a proton is 1.6726 * 10^−27 kg; therefore the acceleration is 613.053318244649049384192275499223 * 10^9 meters per second squared.

The velocity per acceleration gives us the time it took. That is, it took was 1.95741538996306384169271947931375 * 10^-6 sec.
0.00000195741538996306384169271947931375

© It has traveled 2.3488984679556766100312622248235 meters.

(d) The kinetic Energy is (1025.392980096 * 10^-19 N)(2.3488984679556766100312622248235 meters) = 2.40854399999999999999999882043569 * 10^-16 joules.

The book has 6.13 times 10^10 for part a so you did something with the power. For part b the book has 19.6 microseconds so you did something with the power again. For part c the book has an answer of 11.7 meters. And for part d, the book has 1.2 times 10^-15.


This per distance is equal to the constant being 22.5789942664177286497291676228608 * 10^4 meters kilograms per second.
For number 11, the book has 2.25 times 10^-9 N/m as the constant.


All right, now I'm really worried. How am I supposed to do these problems where even a theoretical physicist erred. :(


Oh and by the way, there's another problem set on the next chapter that I have to do. It's gotta be a tough night tomorrow.

[ComradeRed]

For number 29, the book gives an answer of 1.63 times 10^5 N/C. Hmm...what could I have done to be off by 4*10^5? Unless I misappropriated the strength of the string, which is probably where I made my error, I don't see anything with the electromagnetics.

I did, by the by, use the gravitational acceleration for the string as well; I think that I neglected to include the interaction with the charge (gravitation wise).

I'll think about this.



The book has 6.13 times 10^10 for part a so you did something with the power. For part b the book has 19.6 microseconds so you did something with the power again. I goofed with the mass of the proton by 10^3 (I don't deal with conversions what with the Planck scale and all -- don't learn it until grad school! It's too tempting a mistress for anyone too young!).


For part c the book has an answer of 11.7 meters. It should be (613.053318244649049384192275499223 * 10^9)^(
0.00000000195741538996306384169271947931375) which I didn't do.

This is the cause for my other answer to be incorrect.



All right, now I'm really worried. How am I supposed to do these problems where even a theoretical physicist erred. Well, if I told you why, you would never be able to do it right; I have passed the physical rubicon, as it were, (*cough*due to Richard Feynman's Quantum Electrodynamics and the death of the electric field*ahem*) :(

I do suggest learning Maxwell's equations though.

[Janus]

Here are some problems from the electrical energy and capacitance chapter.

15. An electron in the beam of a typical television picture tube is accelerated through a potential difference of 20000 V before it strikes the face of the tube. What is the energy of this electron, in electron volts, and what is its speed when it strikes the screen?

21. A point charge of 9.00 times 10^-9 C is located at the origin. How much work is required to bring a positive charge of 3.00 times 10^-9 C from infinity to the location x=30 cm?

33. A parallel plate capacitor has an area of 2.0 cm^2, and the plates are separated by 2.0 mm with air between them. How much charge does this capacitor store when connected to a 6.0 V battery?

41. Three capacitatoes, C1=5.00 microF, C2=4.00 microF, and C3=9.00 microF, are connected together. (a) Find the effective capacitance of the group is they are parallel. (b) Find the effective capacitance of the group if they are all in series.

48. How should 4 2.0 microF capacitoes be connected to have a total capacitance of (a) 8.0 microF (b) 2.0 microF © 1.5 microF (d) .50 microF

52. 2 capacitors, C1=25 microF and C2=5.0 microF, are connected in parallel and charged with a 100 V power supply. (a) Calculate the total energy stored in the 2 capacitors. (b) What potential difference would be required to across the same two capacitors connected in series in order that the combination store the same energy as in (a)?

[Janus]

Here are the answers for some of the problems listed directly above for reference.

15. 20000 eV, 8.39 times 10^7 m/s

21. 8.10 times 10^-7 J

33. 5.3 times 10^-12 C

41. (a) 18 microF (b) 1.8 microF

[Janus]

It seems that I need some more help with electricity.

4. Find the electric field at a point P(4,4) if a +3 C charge is placed at (0,4) and a -5 C charge is placed at (0,0). Find the electric potential at point P.

6. Calculate the electric potential energy of a proton placed near the surface of a positively charged plate separated from a negatively charged plate by a distance of 1.2 mm. The electric field between the plates is a 1200 V/m uniform field. How fast will the proton be moving just before it hits the negative plate?

8. Find the speed of one of the electrons in the helium atom (atomic radius=31 times 10^-12 m).

9. Find the kinetic energy of the electron in He in eV. Find the potential energy of the electron in He in eV.

[ComradeRed]

15. An electron in the beam of a typical television picture tube is accelerated through a potential difference of 20000 V before it strikes the face of the tube. What is the energy of this electron, in electron volts, and what is its speed when it strikes the screen? Recall that the electrical potential difference ('voltage') between two points is related to the energy that would be required to move a unit of electrical charge from one point to the other against the electrostatic field that is present.

Since we are dealing with a tube of electron-beams, that would be the field's source.

So the distance, i.e. two points, I don't know; the voltage, that is given; and the speed would be the time integral of the acceleration.

There is not enough information.


21. A point charge of 9.00 times 10^-9 C is located at the origin. How much work is required to bring a positive charge of 3.00 times 10^-9 C from infinity to the location x=30 cm?
I assume the 9.00 time 10^-9 C is a positive charge?

Well, that would be equal to the amount of work it would take to move a -3.00 times 10^-9 C from 30cm to infinity.

That is a simple limit (x->infinity) (couloumb's equation) = lim_(dx->infinity) (9*3/(10^18*(dx+.030)^2)) in the canonical units of meters-kilograms-seconds.

This reduces to lim_{dx->infinity} 27/(dx^2 + .006dx + .00009) times coulomb's constant times 10^-18, I'll keep moving (I need to go soon).



33. A parallel plate capacitor has an area of 2.0 cm^2, and the plates are separated by 2.0 mm with air between them. How much charge does this capacitor store when connected to a 6.0 V battery? This is another exercise of capacitance.

A modified version, albeit.

This the permitivity of the thing times the area of the thing divided by the distance between them (approximately). That would be ( 8.8541878176x10-12 F/m.)(.04 m^2)/(.002 m) which is equal to the capacitance.

We then multiply this by the voltage quantity and that is the total charge for both of them.



41. Three capacitatoes, C1=5.00 microF, C2=4.00 microF, and C3=9.00 microF, are connected together. (a) Find the effective capacitance of the group is they are parallel. (b) Find the effective capacitance of the group if they are all in series. What the hell am I an electrical engineer or a theoretical physicist?

(b) C = (5 * 10^-6)^-1 + (4 * 10^-6)^-1 + (9 * 10^-6)^-1

(a) C = (5 * 10^-6) + (4 * 10^-6) + (9 * 10^-6)



48. How should 4 2.0 microF capacitoes be connected to have a total capacitance of (a) 8.0 microF (b) 2.0 microF © 1.5 microF (d) .50 microF I don't have the time! But Parallel is C = C1 + C2 + C3, whereas a series is C = 1/C1 + 1/C2 +...;

Just fiddle around until you get the right amount!



52. 2 capacitors, C1=25 microF and C2=5.0 microF, are connected in parallel and charged with a 100 V power supply. (a) Calculate the total energy stored in the 2 capacitors. (b) What potential difference would be required to across the same two capacitors connected in series in order that the combination store the same energy as in (a)? (a) 50 volts (parallel always have the same voltage).

Capacitors in a parallel configuration each have the same potential difference (voltage).



4. Find the electric field at a point P(4,4) if a +3 C charge is placed at (0,4) and a -5 C charge is placed at (0,0). Find the electric potential at point P. The distance from P to the positive charge X is 4, the distance from P to the negative charge Y is the squareroot of 32 by the Pythagorean theorem.

Plug these equations into coulomb's equations for the two charges independently. That is do it for X by itself (X*X/r^2 times coulomb's constant) and you'll get the force, then multiply it by the distance. Do this for Y too.

Now, they are of different charges and of different distances. I suspect that they will cancel out but I don't know, you need to do the dirty work!

I'm sorry but I need to leave.

[Janus]

So here are the topics for tomorrow's test.

1. System of charges. Incorporating force, electric field, and electric potential.

2. Mechanics/electrostatics

3. Capacitor problems with or without dielectric.

[ComradeRed]

1. System of charges. Incorporating force, electric field, and electric potential. OK, well you know like charges (two positives or two negatives) repel each other and two opposites (positive and negative charge) attract each other, right?

Well, the attraction satisfies coulomb's equation: (constant)(q1)(q2)/(r^2) for charge q1, another charge q2, the distance between them r, and the coulomb constant (approximately 8.988 * 10^9 Newtons-meters^2-per charges squared). This is the force.

The electric field is described by a modification of the equation: (constant)(charge)/(r^2) the whole thing times a unit vector |r2-r1|/(r2-r1) that points from whatever point you are at to the source of the field, the vector is as long as the equation dictates.

The electric potential is (constant)(charge)/®.



2. Mechanics/electrostatics Well, from wikipedia: In electrostatics conditions of charge need not be 'static' and unchanging. Instead 'static' implies that the dynamic portion is being ignored, and we analyze frozen snapshots of the situation. In electrostatics we study e-fields, voltage, and charge but ignore any currents and magnetism which may also be present. Because of its relationship and interaction with magnetism, the two fields are often combined as electromagnetism.

It's largely coulomb's law (- div potential = electric field).




3. Capacitor problems with or without dielectric. Capacitance is charge per volts.

Wikipedia has a great article on Dielectrics (http://en.wikipedia.org/wiki/Dielectrics) in relation to capacitance.

[Janus]

What do I do about the problems that require you to balance the charges. The ones that ask where you would place the charge to make the resultant zero or whatever.

[Janus]

So the book states that the direction of the electric field at a point in space is defined to be the direction of the electric force that would be exerted on a small positive charge at that point. So what exactly does that mean?

Also, if the electric field is zero that means that the system is in equilibrium?

[Janus]

So what exactly is the difference between difference in potential, electric potential, and electric potential energy?
And I still don't understand what electric potential even is. Electric potential energy is just the energy that the charge has due to its position right?

[Janus]

Thanks for your time and generosity, ComradeRed. Hopefully, I'll do better on this test. The next section will probably cover current and resistance, direct current circuits, and maybe magnetism. Just to let you know ahead of time.

[ComradeRed]

So what exactly is the difference between difference in potential, electric potential, and electric potential energy?
And I still don't understand what electric potential even is. Electric potential energy is just the energy that the charge has due to its position right?Physically, potential difference has to do with how much work the electric field does in moving a charge from one place to another.

The electrical potential is the vector potential of the electric field. That is to say take a derivative with respect to r (in polar coordinates, or a divergence of it in cartesian coordinates), and that is the field. It is energy over charge of the field's source.

The potential energy is the energy of that field. That is to say, for a pair of interacting charges, it is coulomb's equation for force multiplied by the distance (or alternatively instead of q1q2 per r^2 take it as q1q2 per r).


So the book states that the direction of the electric field at a point in space is defined to be the direction of the electric force that would be exerted on a small positive charge at that point. So what exactly does that mean?

Also, if the electric field is zero that means that the system is in equilibrium? That force question means that if we took a hypothetical point charge that is positive and placed it near the field's source charge, the direction of the force (remember two opposites attract whereas two likes repel) is based on that interaction.

If the electric field is zero that means there is no charge present.


What do I do about the problems that require you to balance the charges. The ones that ask where you would place the charge to make the resultant zero or whatever. What you have to do is figure out the force acting that you have to counterbalance. Then (usually a charge is given) and you need to figure out the electric force to counteract the other force.

You could set coulomb's equation to the resulting force needing to be counterbalanced, then use math on it.