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Question

A conducting sphere of radius 10 cm has an unknown charge. If the electric field 20 cm from the centre of the sphere is 1.5×103 N/C and points radially inward, what is the net charge on the sphere?

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Solution

Step 1: Electric field outside a conducting sphere
E=14π0qr2
where r is the distance from the centre of conducting sphere.

q=4π0E r2 ....(1)

Step 2: Substituting the values

q=19×109×1.5×103N/C×(0.2m)2=6.67×109C=6.67nC
Because the electric field lines point radially inwards, the nature of the charge on the sphere is negative.
Therefore q=6.67nC


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