Question

a non conducting ring of radius r = 10 cm has linear charge density lambda = 2cos(0/2)*10^-10c/m as shown in figure the potential at the ring in volt is​

Answer 1

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Answer 2

Consider two small elements of length dl=Rdθ symmetrically at angle θ on both sides as shown in the figure. Here, dE  

1 =dE

2

and sin component cancel out each other. Charge on the element , dq=λdl=(λ 0cosθ)Rdθ

Net field at center due to both elements , dE=2dE 1 cosθ=2( 4πϵ 0 R 2 dq )cosθ= 4πϵ 0 R λ 0 2cos 2 θdθ

or

E= 4πϵ 0 R λ 0 ∫ 0 π (1+cos2θ)dθ= 4πϵ 0 R λ 0 [(π−0)+ 2 1 (sin2π−sin0)]= 4ϵ 0 R λ 0

thus, x=4

Therefore the potential of the ring in volt is 4.