Let there be a spherically symmetric charge distribution with charge density varying as (r )= _0( 54- rR) upto r = R, and ρ(r) = 0 for r R, where r is the distance from the origin. The electric fie…

Question

Let there be a spherically symmetric charge distribution with charge density varying as (r )= _0( 54- rR) upto r = R, and ρ(r) = 0 for r > R, where r is the distance from the origin. The electric field at a distance r (r < R) from the origin is given by

Accepted Answer

Correct answer: B. (b) Consider a spherical shell of radius x and thickness dx. Charge on it dq dq = ρ × 4πx2. dx dq = ρ0 ( 54- xR) x 4πx2 dx q = 4πρ0 ( 5x^24- x^3R) dx q = 4 ρ0 ( 5r^33 4- r^44R) E = kqr^2 = 14 r^2 × 4πρ0 ( 5r^33 4- r^44R) E = ρ_0r4 ρ_0 ( 53- rR)

$Let there be a spherically symmetric charge distribution with charge density varying as ρ (r) = ρ_{0} (\frac{5}{4} - \frac{r}{R}) upto r = R, and ρ(r) = 0 for r > R, where r is the distance from the origin. The electric field at a distance r (r < R) from the origin is given by$

Solution

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