Three nested hollow spheres have the same center. The innermost sphere has a rad

Question

Three nested hollow spheres have the same center. The innermost sphere has a radius of 4 cr and carries a uniformly distributed charge of 6 n n 6 cm and carries a uniformly distributed charge of -4 nC. The outermost sphere has a radius of 9 cm and carries a uniformly distributed charge of 8 nC 1 x 10 The middle sphere asa radius of (a) What is the magnitude of the electric feld at a distance of 3 cm from the center? N/C (b) What is the magnitude of the electric field at a distance of 5 cm from the center? N/C c) What is the magnitude of the electric field at a distance of 7 cm from the center? N/C

Explanation / Answer

A.

we know that electric field inside a hollow sphere is zero.

Since at distance of 3 cm from the center is inside all the three spheres, So

E(r = 3) = 0 N/C

B.

Electric field outside sphere is given by:

E = kQ/R^2

a distance of 5 cm from the center is outside the first sphere and inside the middle and outermost sphere, So

Enet = Ei + Em + Eo

Enet = kQ/R^2 + 0 + 0

Enet = 9*10^9*6*10^-9/0.05^2

Enet = 21600 N/C

C.

a distance of 7 cm from the center is outside the inner and middle sphere and inside the outermost sphere, So

Enet = Ei + Em + Eo

Enet = kQ1/R^2 + kQ2/R^2 + 0

Enet = 9*10^9*6*10^-9/0.07^2 - 9*10^9*4*10^-9/0.07^2

Enet = 3673.47 N/C

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