A) a total charge q = 23.6 μc is deposited uniformly on the surface of a hollow sphere with radius r = 26.1 cm. use ε0 = 8.85419 x 10−12 c2/nm2. what is the magnitude of the electric field at the center of the sphere? b) what is the magnitude of the electric field at a distance r/2 from the center of the sphere? c) what is the magnitude of the electric field at a distance 52.2 cm from the center of the sphere?

(a) E = 0 N/C

(b) E = 0 N/C

(c) E = 7.78 x10^5 N/C

Explanation:

We are given a hollow sphere with following parameters:

Q = total charge on its surface = 23.6 μC = 23.6 x 10^-6 C

R = radius of sphere = 26.1 cm = 0.261 m

Permittivity of free space = ε0 = 8.85419 X 10−12 C²/Nm²

The formula for the electric field intensity is:

E = (1/4πεo)(Q/r²)

where, r = the distance from center of sphere where the intensity is to be found.

(a)

At the center of the sphere r = 0. Also, there is no charge inside the sphere to produce an electric field. Thus the electric field at center is zero.

E = 0 N/C

(b)

Since, the distance R/2 from center lies inside the sphere. Therefore, the intensity at that point will be zero, due to absence of charge inside the sphere (q = 0 C).

E = 0 N/C

(c)

Since, the distance of 52.2 cm is outside the circle. So, now we use the formula to calculate the Electric Field:

E = (1/4πεo)[(23.6 x 10^-6 C)/(0.522m)²]

E = 7.78 x10^5 N/C

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