[12] A solid ball of radius R has a charge density given by = ₀ (1- r R ) for 0 r R . The electric field outside the ball is:

Step-by-step solution

Charge density, = ₀ (1- r R ) aligned &d q= d v &q_ in = d q= d v &= ₀ (1- r R ) 4 r^2 d r ( d v=4 r ^2 dr ) &=4 ₀ ₀^R (1- r R ) r^2 d r &=4 ₀ ₀^R r^2 d r- r^2 R d r &=4 ₀ [ [ r^3 3 ]₀^R- [ r^4 4 R ]₀^R ] &=4 ₀ [ R^3 3 - R^4 4 R ] aligned =4 ₀ [ R^3 3 - R^3 4 ]=4 ₀ [ R^3 12 ]q= ₀ R^3 3 E .4 r^2= ( ₀ R^3 3 ₀ ) Electric field outside the ball, E= ₀ R^3 12 ₀ r^2