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A nonconducting solid sphere of radius 2.80 cm carries a uniformly distributed positive charge of 8.70�10-9 C. Calculate the magnitude of the electric field at a point 1.90 cm away from the center of the sphere.

Calculate the magnitude of the electric field at a point 3.90 cm away from the center of the sphere.

Assume that the sphere is conducting. Calculate the magnitude of the electric field at a point 1.90 cm away from the center of the sphere.

Calculate the magnitude of the electric field for the conducting sphere at a point 3.90 cm away from the center of the sphere.  Edit Comment  Solutions
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Radius of sphere, r = 2.8 cm = 0.028 m

Volume of sphere, V = 4/3*pi*r3

Charge on sphere = 8.7*10-9 C

Imagine a gaussian surface of a sphere with radius 1.9 cm

Charge contained in the small sphere with radius 1.9 cm = (Total charge/Total volume)*small sphere volume =

8.7*10-9*(2.83/1.93) = 2.71*10-9 C

Thus, for this surface we have :

EA = Q/\epsilono

Here, E is electric field at gaussian surface, A is surface area of gaussian surface, Q is charge contained in the surface

A = 4*pi*0.0192 = 4.53*10-3 m2

Thus putting values we get, E = 67.59 kN/m

Electric field at 3.9 cm distance = k*8.7*10-9/0.0392 = 51.47 kN/m

If the sphere is conducting, all the charge is at the surface, thus electric field at 1.9 cm from centre is 0

At 3.9 cm distance, electric field is same as the previous case because in this case also we can treat the sphere as a point charge since the location is outside the sphere  Edit Comment  Close Choose An Image
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