Question

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. What is the maximum magnitude of the electric field due to this sphere?

Answer 1

Answer:

$E_{max}=41666.66\ N/C$

Explanation:

Given that,

The radius of sphere, r = 0.3 m

Distance from the center of the sphere to the point P, x = 0.5 m

Electric field at point P, $E_P=15000\ N/C$ (radially outward)

The maximum electric field is at the surface of the sphere. We know that the electric field is inversely proportional to the distance. So,

$\dfrac{E_{max}}{E_p}=\dfrac{0.5^2}{0.3^2}$

$\dfrac{E_{max}}{15000}=\dfrac{0.5^2}{0.3^2}$

${E_{max}}=\dfrac{0.5^2}{0.3^2}\times 15000$

$E_{max}=41666.66\ N/C$

So, the magnitude of the electric field due to this sphere is 41666.66 N/C. Hence, this is the required solution.