The electric potential immediately outside a charged conducting sphere is 190 V,

Question

The electric potential immediately outside a charged conducting sphere is 190 V, and 10.0 cm farther from the center of the sphere the potential is 140 V. Determine the radius of the sphere. cm Determine the charge on the sphere. nC The electric potential immediately outside another charged conducting sphere is 200 V, and 10.0 cm farther from the center the magnitude of the electric field is 410 V/m. Determine all possible values for the radius of the sphere. (Enter your answers from smallest to largest. If only one value exists, enter "NONE" in the second answer blank.) r_1 = Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. cm r_2 = The response you submitted has the wrong sign. cm Determine the charge on the sphere for each value of r. (If only one value exists, enter "NONE" in the second answer blank.) q_1 = nC q_2 = nC

Explanation / Answer

electric potential outside the sphere = 200 V

electric field 10 cm outside the sphere = 410 V/m

electric potential = k * q / r

200 = 9 * 10^9 * q / r -------(1)

electric field = k * q / (r + 0.1)^2

410 = 9 * 10^9 * q / (r + 0.1)^2 --------(2)

on solving equation 1 and 2 we'll get

r = 0.0404 m or 0.247 m and

q = 8.983 * 10^-10 C or 5.497 * 10^-9 C

so,

r1 = 0.0404 m

r2 = 0.247 m

charge on the sphere for each value of r

q1 = 0.8983 nC

q2 = 5.497 nC

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