Find the electric field at a point outside of an insulating sphere?

In summary, the question asks for the electric field at a point 0.12m outside the surface of an isolated plastic sphere with a diameter of 0.23m. Using the formula E = kQ/(r^2), the charge of the sphere was determined to be 1.98375*10^-9C. Treating the sphere as a point charge, the distance used in the formula for the electric field was not correct, resulting in an incorrect answer of 1239.8 N/C.
  • #1
hockey
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Homework Statement


What is the electric field at a point .12m outside the surface of an isolated plastic sphere .23m in diameter that produces an electric field of 1350 N/C just outside the surface of the sphere?


Homework Equations


E = kQ/(r^2)


The Attempt at a Solution


First I found Q for the sphere with the above formula by substitution and found that it was 1.98375*10^-9C. From there, I thought that I could treat the sphere as a point charge and use the same formula to find the electric field, substituting as follows:
E= (9*10^9 Nm^2/C^2) (1.98375*10^-9C)/(.12m)^2 and got a result of 1239.8 N/C. This is not correct however, and I am not sure if it is because I am viewing the question wrong or not.
 
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  • #2
hockey said:

Homework Statement


What is the electric field at a point .12m outside the surface of an isolated plastic sphere .23m in diameter that produces an electric field of 1350 N/C just outside the surface of the sphere?


Homework Equations


E = kQ/(r^2)


The Attempt at a Solution


First I found Q for the sphere with the above formula by substitution and found that it was 1.98375*10^-9C. From there, I thought that I could treat the sphere as a point charge and use the same formula to find the electric field, substituting as follows:
E= (9*10^9 Nm^2/C^2) (1.98375*10^-9C)/(.12m)^2 and got a result of 1239.8 N/C. This is not correct however, and I am not sure if it is because I am viewing the question wrong or not.

Yes, you can treat the charged sphere as a point charge. But take a closer look at what you used as the distance from that charge for your second calculation. That distance was specified to be 0.12m outside of the original sphere... so where does that put it with respect to the "new" point charge?
 
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1. What is the formula for finding the electric field at a point outside of an insulating sphere?

The formula for finding the electric field at a point outside of an insulating sphere is given by E = kQ/r2, where k is the Coulomb's constant, Q is the charge of the sphere, and r is the distance from the center of the sphere to the point where the electric field is being measured.

2. How does the electric field at a point outside of an insulating sphere vary with distance?

The electric field at a point outside of an insulating sphere decreases as the distance from the center of the sphere increases. This is because the electric field is inversely proportional to the square of the distance from the center of the sphere, according to the formula E = kQ/r2.

3. Can the electric field at a point outside of an insulating sphere be negative?

No, the electric field at a point outside of an insulating sphere cannot be negative. This is because an insulating sphere has a net charge of zero, so the electric field lines always point away from the sphere in all directions, resulting in a positive electric field at all points outside the sphere.

4. How does the electric field at a point outside of an insulating sphere change if the charge of the sphere is doubled?

If the charge of the insulating sphere is doubled, the electric field at a point outside of the sphere will also double. This is because the electric field is directly proportional to the charge of the sphere, according to the formula E = kQ/r2.

5. Can the electric field at a point outside of an insulating sphere be affected by the material of the sphere?

No, the electric field at a point outside of an insulating sphere is not affected by the material of the sphere. This is because the material of the sphere does not have any impact on the net charge of the sphere, which is the only factor that affects the electric field at a point outside of the sphere.

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