Consider a uniformly charged non conducting, spherical shell of radius R. Net charge on the shell is Q . There is a small hole in the shell at 'A' shown in the figure. A point charge -q is r

Question

Consider a uniformly charged non conducting, spherical shell of radius R. Net charge on the shell is Q . There is a small hole in the shell at 'A' shown in the figure. A point charge -q is released at a distance 2R from the centre as shown in the figure. The shell and point charge have same mass m . After release the point charge will move toward shell, passes through the hole and hit the shell at ' $B$ '. (consider $k = \frac{1}{4 π ϵ _{0}}$ )

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TestHub · Accepted Answer

(A) m ( 3 R − X ) − mx = 0 ⇒ x = 2 3 R ​ (B) By conservation of energy 2 × 2 1 ​ m v 1 2 ​ − R k Qq ​ = 2 R − k Qq ​ , m v 1 2 ​ = 2 r k Qq ​ ⇒ v 1 ​ = 2 m R k Qq ​ ​ (C) t AB ​ = 2 2 mR kQq ​ ​ 2 R ​ = kQq 2 mR 3 ​ ​ (D) Total distance covered by shell and particle with constant velocity is 2 R , therefore distance covered by shell with constant velocity is R .

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JEE Advanced 2027 (Class 12)