A uniformly charged sphere is placed inside a charged hollow non-conducting sphere as shown in figure. O is the centre of hollow sphere and C is the centre of solid sphere. The magnitude of charge on

Question

A uniformly charged sphere is placed inside a charged hollow non-conducting sphere as shown in figure. O is the centre of hollow sphere and C is the centre of solid sphere. The magnitude of charge on both the spheres is 4 ( 7 3 ​ ​ ) μ C . The electric field at point ' P ' which lie just outside the hollow sphere is given by E × 1 0 3 N / C . Find the value of E .

TestHub · Accepted Answer

OP = O C 2 + C P 2 ​ = 3 + 1 ​ = 2 m, and ∠ OPC = 6 0 ∘ . At P (just outside both spheres): the hollow sphere contributes O P 2 k q ​ = 4 k q ​ along OP; the solid sphere contributes C P 2 k q ​ = k q along CP. E 2 = ( k q ) 2 [ 16 1 ​ + 1 + 2 × 4 1 ​ cos 6 0 ∘ ] = ( k q ) 2 × 16 21 ​ . k q = 9 × 1 0 9 × 4 7 3 ​ ​ × 1 0 − 6 = 3.6 × 1 0 4 7 3 ​ ​ , so E = 4 3.6 × 1 0 4 ​ 7 3 ​ × 21 ​ = 9 × 1 0 3 × 3 = 27 × 1 0 3 N/C ⇒ E = 27.

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