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Phantasy [73]
3 years ago
13

A solid nonconducting sphere of radius R carries a charge Q distributed uniformly throughout its volume. At a certain distancer1

(r1< R) from the center of the sphere, the electric field has magnitude E. If the same charge Q were distributed uniformly throughout a sphere of radius 2R, the magnitude of the electric field at the same distancer1 from the center would be equal to ___________.
Physics
1 answer:
Jobisdone [24]3 years ago
4 0

Answer:

The magnitude of the electric field in the second case will be \frac{1}{8} of the electric field in the first case

Explanation:

The electric field at a distance r_1 < R from the center of the sphere is given by

the formula E_1  = \frac{kQr_1}{R^3}  

where R is the radius of the sphere, and, Q is the charge uniformly distributed on the sphere.

It is given that the same charge Q is distributed uniformly throughout a sphere of radius 2R and we have to find the electric field at same distance r_1 from the center.

In the second case the electric field will be given by

E_2 = \frac{kQr_1}{(2R)^3}  = \frac{kQr_1}{8R^3}  =\frac{1}{8}  \frac{kQr_1}{R^3} = \frac{1}{8} E_1

Therefore the magnitude of the electric field in the second case will be \frac{1}{8} of the electric field in the first case.

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