The region between two concentric spheres of radii 'a' and 'b', respectively (see figure), has volume charge density ρ = A r , where A is a constant and r is the distance from the centre. At the centre of the spheres is a point charge Q. The value of A such that the electric field in the region between the spheres will be constant, is:

Question

The region between two concentric spheres of radii 'a' and 'b', respectively (see figure), has volume charge density ρ = A r , where A is a constant and r is the distance from the centre. At the centre of the spheres is a point charge Q. The value of A such that the electric field in the region between the spheres will be constant, is:, 2 Q π a 2 - b 2, 2 Q π a 2, Q 2 π a 2, Q 2 π b 2 - a 2

MARKS App · Accepted Answer

E=E 1 + E 2 ⇒E = K Q + ∫ a r 4 π x 2 d x A x r 2 E = K Q r 2 + 4 π A r 2 2 r 2 - a 2 2 r 2 d E d r = 0 ⇒ - 2 Q r 3 + 8 π A a 2 2 r 3 = 0 A = Q 2 π a 2

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