# Electric charge is distributed inside a nonconducting sphere

## Homework Statement

Electric charge is uniformly distributed inside a nonconducting sphere of radius 0.30 m. The electric field at a point P, which is 0.50 m from the center of the sphere, is 15,000 N/C and is directed radially outward. At what distance from the center of the sphere does the electric field have the same magnitude as it has at P?

E = KQ * (1/r^2)

## The Attempt at a Solution

So I tried using the equation E = KQ * (1/r^2) but I'm not given a charge. What should I do? Is finding the charge of P helpful??? Does the charge not matter in this case and I'm just using the wrong equation?

SammyS
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## Homework Statement

Electric charge is uniformly distributed inside a nonconducting sphere of radius 0.30 m. The electric field at a point P, which is 0.50 m from the center of the sphere, is 15,000 N/C and is directed radially outward. At what distance from the center of the sphere does the electric field have the same magnitude as it has at P?

E = KQ * (1/r^2)

## The Attempt at a Solution

So I tried using the equation E = KQ * (1/r^2) but I'm not given a charge.
You should be able to use that to determine the total amount of charge, and thus the charge density. Right?

What should I do? Is finding the charge of P helpful??? Does the charge not matter in this case and I'm just using the wrong equation?

haruspex
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So I tried using the equation E = KQ * (1/r^2) but I'm not given a charge. What should I do? Is finding the charge of P helpful??? Does the charge not matter in this case and I'm just using the wrong equation?
Often you just have to create an unknown then see what equations you can involve it in.
Let the charge density be ρ. In terms of that, what should the electric field at P be?

collinsmark
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## Homework Statement

Electric charge is uniformly distributed inside a nonconducting sphere of radius 0.30 m. The electric field at a point P, which is 0.50 m from the center of the sphere, is 15,000 N/C and is directed radially outward. At what distance from the center of the sphere does the electric field have the same magnitude as it has at P?

E = KQ * (1/r^2)

## The Attempt at a Solution

So I tried using the equation E = KQ * (1/r^2) but I'm not given a charge.
You could use that equation to solve for the charge (as a function of E), but I think you'll find that it's not particularly useful.

What should I do? Is finding the charge of P helpful??? Does the charge not matter in this case and I'm just using the wrong equation?

Here are some pointers to get you started.

• Like @haruspex suggests, express the charge as a function of the charge density $\rho$, and the volume of the sphere.
• Find an expression for electric field inside the sphere. Have you studied Gauss' Law yet? If you are allowed to use Gauss' Law, it makes the problem a lot easier.
• If at any point you wish to invoke Coulomb's law, don't use the version with "k". Instead, use the $E = \frac{1}{4 \pi \varepsilon_0} \frac{q}{r^2}$ version.

SammyS
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Am I reading a different problem than others are?
• The charge is uniformly distributed over the sphere's volume.
• The magnitude of the electric field is given at a point external to the sphere.
It's clear that the total charge of the sphere can then be obtained immediately. Together with the dimensions of the sphere one readily obtains the charge density.

collinsmark
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Am I reading a different problem than others are?
• The charge is uniformly distributed over the sphere's volume.
• The magnitude of the electric field is given at a point external to the sphere.
It's clear that the total charge of the sphere can then be obtained immediately. Together with the dimensions of the sphere one readily obtains the charge density.
Correct!

I'm just saying that solving for the total charge (or even numerically calculating the charge density) isn't necessarily that useful in obtaining the final answer to the problem. Sure, one can do it, but it just doesn't really matter that much.

SammyS
• Like @haruspex suggests, express the charge as a function of the charge density ρρ \rho , and the volume of the sphere.
• Find an expression for electric field inside the sphere. Have you studied Gauss' Law yet? If you are allowed to use Gauss' Law, it makes the problem a lot easier.
• If at any point you wish to invoke Coulomb's law, don't use the version with "k". Instead, use the E=14πε0qr2E=14πε0qr2 E = \frac{1}{4 \pi \varepsilon_0} \frac{q}{r^2} version.
I don't understand how to get the charge density though and it's not even given to me in the problem, so how is that helpful?

haruspex
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I don't understand how to get the charge density though and it's not even given to me in the problem, so how is that helpful?
You do know the field at a certain point. If you can also obtain an expression for what that field ought to be based on the (unknown) charge (or charge density) then that will give you an equation.

collinsmark
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I don't understand how to get the charge density though and it's not even given to me in the problem, so how is that helpful?
Perhaps I wasn't clear in my previous post. What I was trying to say is that putting effort into finding the numerical value of the charge or charge density is not helpful (although it's not harmful) in solving this particular problem. It couldn't hurt, but it won't help either.

If it aids in understanding, consider a simple pendulum. Its period is independent of the pendulum's mass. If you were given a problem to derive its period you could first calculate the numerical value of the pendulum's mass if sufficient information was given to you. But it wouldn't really help you to find its period. The simplest approach is just to call the mass of the pendulum m and leave it at that. This problem is kind of along those lines.