Anon conducting sphere of radius 0.04 m has a charge of 5.0 × 10^-9 c deposited on it. calculatethe magnitude of the electric field at 0.02m from the center of the sphere

The electric field at a distance r = 0.02 m is 14062.5 N/C.

Solution:

Refer to fig 1.

As per the question:

Radius of sphere, R = 0.04 m

Charge, Q =

Distance from the center at which electric field is to be calculated, r = 0.02 m

Now,

According to Gauss' law:

Now, the charge enclosed at a distance r is given by volume charge density:

Also, the charge enclosed Q' at a distance r is given by volume charge density:

Since, the sphere is no-conducting, Volume charge density will be constant:

Thus

Thus charge enclosed at r:

Now, By using Gauss' Law, Electric field at r is given by:

Thus

E = 14062.5 N/C

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pythagoras' theorem

square root (-5^2+9^2)

square root (25+81)

square root (106)

angle is tan^-1(9/5)

neg x, pos y