Electrostatistics charges and electric potential problem

[VanKwisH]

Homework Statement

A +30uc charge is placed 60cm from an identical +30uc charge. how much work would be required to move a +0.2uc test charge from a point midway between them to a point 10 cm close to either of the charges

Homework Equations

E = F/Q = KQ / r^2
E= V/D
W = PE = V*Q = Kq1q2 / r

The Attempt at a Solution

I know that work moving the test charge either way should be equal.
First step should i be finding the electric potential on both +30uc charges?
and the find the total electric field?

 

[jandl]

Think about what is happening here:

All of the charges are repulsive. Assume the that two larger charges are not going to move and only worry about what is happening with the little charge.

When the little charge is in the middle it is being pushed away from both of the larger charges by the same amount. When you move the little one, call the charge you move it towards charge A and the farther one charge B. When you move it towards A, A starts pushing on the little guy more, so it would require some energy (some work) to do this. But as you move the little charge away from B, you are gaining some energy. With the equations you've written you should be able to calculate these energies.

Another way to think about this problem is to consider the potential energy of the little charge in its initial and final positions. You need to determine which position has a higher potential. If you can do this, you pretty much have your answer.

Think about these things and hopefully you'll understand the situation enough that the relevant equations will be clear. Let us know if you still have questions.

 

[Moetasim]

Yes, to solve this problem, you will need to find the electric potential at both +30uc charges and then use that to calculate the total electric field. From there, you can use the equation W = PE = V*Q to find the work required to move the test charge. Here is a step-by-step solution:

1) Calculate the electric potential at each +30uc charge using the formula V = kQ/r. Plugging in the values, we get V = (9x10^9)(30x10^-6)/0.6 = 4.5x10^5 V.

2) Since the test charge is midway between the two +30uc charges, it will experience equal and opposite forces from each charge. This means that the electric field at this point will be zero.

3) Now, we need to find the electric potential at the point where the test charge will be moved to. Since it will be 10cm closer to either of the charges, the distance from the test charge to the other +30uc charge will be 0.5cm. Using the same formula as before, we get V = (9x10^9)(30x10^-6)/0.005 = 5.4x10^7 V.

4) To find the total electric field, we need to add the individual electric fields at that point. Since the electric field at the midway point was zero, the total electric field will simply be the electric field at the point where the test charge will be moved to. So the electric field will be E = 5.4x10^7 V/0.005 = 1.08x10^10 V/m.

5) Now, we can use the equation W = PE = V*Q to find the work required to move the test charge. Since the test charge is +0.2uc, we can plug in the values and get W = (1.08x10^10 V/m)(0.2x10^-6 C) = 2.16x10^4 J.

Therefore, the work required to move the test charge from the midway point to a point 10cm closer to either charge is 2.16x10^4 J.