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
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Answer:
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
0
cosθ)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
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