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Question

# Let E1(r),E2(r) and E3(r) be the respective electric fields at a distance r from a point charge Q, an infinitely long wire with constant linear charge density λ, an infinite plane with uniform surface charge density σ. If E1(r0)=E2(r0)=E3(r0) at a given distance r0, then

A
Q=4σπr20
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B
r0=λ2πσ
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C
Q=2σπr20
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D
r0=λπσ
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Solution

## The correct options are C Q=2σπr20 D r0=λπσ Electric field at a distance r from a point charge Q is given by E=kQr2 ∴E1=kQr20 Electric field at a distance r from an infinitely long wire of linear chage density λ is given by E=λ2πϵ0r ∴E2=λ2πϵ0r0 Electric field at a distance r from an infinite plane of surface chage density σ is given by E=σ2ϵ0 ∴E3=σ2ϵ0 Given E1=E2=E3 E1=E3⇒kQr20=σ2ϵ0 ⇒Q=r2ok×σ2ϵ0 ⇒Q=r2o×4πϵ0×σ2ϵ0 (∵k=14πϵ0) ⇒Q=2πσr20 (c) Also, E2=E3⇒λ2πϵ0r0=σ2ϵ0 ⇒r0=λπσ (d)

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