Let there be a spherically symmetric charge distribution with charge density varying as (r)= ₀ ( 5 4 - r R ) upto r=R , and (r)=0 for rR , where r is the distance from the origin. The electric field at a distance r(r

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Let there be a spherically symmetric charge distribution with charge density varying as (r)= ₀ ( 5 4 - r R ) upto r=R , and (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

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Correct answer: B. ₀ r 4 ₀ ( 5 3 - r R )

Apply shell theorem the total charge upto distance r can be calculated as followed d q=4 r^2 d r . aligned & =4 r^2 d r ₀ [ 5 4 - r R ] & =4 ₀ [ 5 4 r^2 d r- r^3 R d r ] & d q=q=4 ₀ ₀^r ( 5 4 r^2 d r- r^3 R d r ) & =4 ₀ [ 5 4 r^3 3 - 1 R r^4 4 ] & E= k q r^2 & = 1 4 ₀ 1 r^2 4 ₀ [ 5 4 ( r^3 3 )- r^4 4 R ] & E= ₀ r 4 ₀ [ 5 3 - r R ] & aligned

Let there be a spherically symmetric charge distribution with charge density varying as (r)= ₀ ( 5 4 - r R ) upto r=R , and (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

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