Solving Electric Magnetism Problems: Forces, Fields, Potentials, Work

[brains]

I need some help figuring #2 problem out.

Homework Statement

1. two charges of 6 microcoulombs and 10 microcoulombs are 10cm apart. Calculate their force of repulsion. Calculate the electric field midway between them.
2. For the charges in question 1 calculate the potential midway between them. Calculate the work to bring an electron from far away to midway between them.
So for the first question I used F= k |q1||q2|/r^2 for the second part of the first question i did E = k |q|/r^2

i calculated that the force would be 53.94N
As for the electric midway I calculate it to 3.6 x 10^6 N/c Although I am not sure if i was supposed to add or subtract E1 and E2. So what i did is that i subtracted. But I am not entirely sure if that is my correct answer My work:
E1 = 8.99x 10^9 N*m^2/c^2 x |6 x10^-6 C|/(0.1m)^2

E1 = 5.39 x 10^6 N/c is my answer for E1

E2 = 8.99 x 10^9 N*m^2/c^2 x |10 x 10^-6C|/(0.1m)^2

E2 = 8.99 x 10 ^6 N/C

Then i did E = 8.99 x 10^6 N/C - 5.39 X 10^6 N/C
And I got 3.6 x 10^6 N/C however like i said before I am not exactly sure if this was the correct approach to get the electric field midwayFor the second question
I used this equation (U= k (q0)(q)/r ---> k being 8.99 x10^9n.m^2/c^2 for part of the 1st question in question 2 that asks for potential midway and got an answer of U= 10.78 N M

however when they asked me for the work in question two i assumed I should have used -W=q0Ed
but i don't know what numbers I would use for this equation. Would the correct way of going about it be
doing -W=(1.60 x 10^-19C)(8.99 x 10^6 N/C - 5.39 X 10^6 N/C)(0.1m) or is this wrong?

IF someone could please point me in the right direction and check if I've done these steps correctly it would be helpful. Thank you in advance.

 

[majormaaz]

I need some help figuring #2 problem out.

Homework Statement

1. two charges of 6 microcoulombs and 10 microcoulombs are 10cm apart. Calculate their force of repulsion. Calculate the electric field midway between them.



2. For the charges in question 1 calculate the potential midway between them. Calculate the work to bring an electron from far away to midway between them.



So for the first question I used F= k |q1||q2|/r^2 for the second part of the first question i did E = k |q|/r^2

i calculated that the force would be 53.94N
As for the electric midway I calculate it to 3.6 x 10^6 N/c Although I am not sure if i was supposed to add or subtract E1 and E2. So what i did is that i subtracted. But I am not entirely sure if that is my correct answer


My work:
E1 = 8.99x 10^9 N*m^2/c^2 x |6 x10^-6 C|/(0.1m)^2

E1 = 5.39 x 10^6 N/c is my answer for E1

E2 = 8.99 x 10^9 N*m^2/c^2 x |10 x 10^-6C|/(0.1m)^2

E2 = 8.99 x 10 ^6 N/C

Then i did E = 8.99 x 10^6 N/C - 5.39 X 10^6 N/C
And I got 3.6 x 10^6 N/C however like i said before I am not exactly sure if this was the correct approach to get the electric field midway


For the second question
I used this equation (U= k (q0)(q)/r ---> k being 8.99 x10^9n.m^2/c^2 for part of the 1st question in question 2 that asks for potential midway and got an answer of U= 10.78 N M

however when they asked me for the work in question two i assumed I should have used -W=q0Ed
but i don't know what numbers I would use for this equation. Would the correct way of going about it be
doing -W=(1.60 x 10^-19C)(8.99 x 10^6 N/C - 5.39 X 10^6 N/C)(0.1m) or is this wrong?

IF someone could please point me in the right direction and check if I've done these steps correctly it would be helpful. Thank you in advance.

Hey there!

So for the first question I used F= k |q1||q2|/r^2 for the second part of the first question i did E = k |q|/r^2

i calculated that the force would be 53.94N

Yep. That's right.

As for the electric midway I calculate it to 3.6 x 10^6 N/c Although I am not sure if i was supposed to add or subtract E1 and E2. So what i did is that i subtracted. But I am not entirely sure if that is my correct answer


My work:
E1 = 8.99x 10^9 N*m^2/c^2 x |6 x10^-6 C|/(0.1m)^2

E1 = 5.39 x 10^6 N/c is my answer for E1

E2 = 8.99 x 10^9 N*m^2/c^2 x |10 x 10^-6C|/(0.1m)^2

E2 = 8.99 x 10 ^6 N/C

Then i did E = 8.99 x 10^6 N/C - 5.39 X 10^6 N/C
And I got 3.6 x 10^6 N/C however like i said before I am not exactly sure if this was the correct approach to get the electric field midway

You're almost correct here - I'd say to take a look at your value for r again. As in, what are you measuring r to be again?


As for both parts of the second question:

I used this equation (U= k (q0)(q)/r
...i assumed I should have used -W=q0Ed

The formula for U is for electrical potential energy, not the potential. But - there's a relationship between the two quantities, as well as one between W and U. Once you find those out, you're good to go.

 

[brains]

You're almost correct here - I'd say to take a look at your value for r again. As in, what are you measuring r to be again?

Well I take the idea it's 10cm i converted that into 0.1m. Um I am guessing since they are asking me to calculate the electron from far away to midway. I would only take into account half of the original distance right?

 

[brains]

You're almost correct here - I'd say to take a look at your value for r again. As in, what are you measuring r to be again?

Well I take the idea it's 10cm i converted that into 0.1m. Um I am guessing since they are asking me to calculate the electron from far away to midway. I would only take into account half of the original distance right?

 

[majormaaz]

Well I take the idea it's 10cm i converted that into 0.1m. Um I am guessing since they are asking me to calculate the electron from far away to midway. I would only take into account half of the original distance right?

In regards to the Electric field problem, the question asks for the electric field at the midway point between the two charges. A radius of 10 cm here would imply that the point in question is at either charge.

With respect to the Potential Energy, yes. To be more technical, it's ΔU = U_f - U₀, and if you use an r = ∞ for U_f, that expression becomes just -U₀.

 

[brains]

Sorry for the late reply and thank you very much i finally understood it :D.