In a conducting hollow sphere of inner and outer radii $$5$$ cm and $$10$$ cm, respectively, a point charge $$1$$ C is placed at point A, that is $$3$$ cm from the center C of the hollow sphere. An external uniform electric field of magnitude $$20$$ NC−$$1$$ is also applied. Net electric force on this charge is $$15$$ N, away from the center of the sphere as shown. Find the magnitude of net force exerted on the charge placed at point A by the induced charges on the sphere.

Question

In a conducting hollow sphere of inner and outer radii $$5$$ cm and $$10$$ cm, respectively, a point charge $$1$$ C is placed at point A, that is $$3$$ cm from the center C of the hollow sphere. An external uniform electric field of magnitude $$20$$  NC−$$1$$ is also applied. Net electric force on this charge is $$15$$ N, away from the center of the sphere as shown. Find the magnitude of net force exerted on the charge placed at point A by the induced charges on the sphere.

Infinity Learn · Accepted Answer

External applied field's effect is neutralized by charge induced on outer surface, i.e., their combined effect is zero. Hence, force applied by induced charges on outer surface should be equal and opposite to that applied by electric field. This is equal to $$qE=1$$×$$20$$  N toward left. $$15$$ N force is only due to induced charge on the inside surface of the hollow sphere. Hence, net force by induced charges is $$15$$ $$+$$ $$20$$ $$=$$ $$35$$ N.

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