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Physics-Electric Field

NEET Physics Electric Field MCQ Question

Type: MCQ-numerical-Medium-Class 12

A long straight wire carries a uniform linear charge density λ\lambda. Using Gauss's law, what is the magnitude of the electric field EE at a perpendicular distance rr from the wire?

A

λ2πϵ0r\frac{\lambda}{2\pi\epsilon_0 r}

B

λ4πϵ0r2\frac{\lambda}{4\pi\epsilon_0 r^2}

C

2λπϵ0r\frac{2\lambda}{\pi\epsilon_0 r}

D

λ4πϵ0r\frac{\lambda}{4\pi\epsilon_0 r}

Correct Answer

Option A

Detailed Explanation

According to Gauss's law, the electric field EE for a long straight wire with uniform charge density λ\lambda at a distance rr is given by E=λ2πϵ0rE = \frac{\lambda}{2\pi\epsilon_0 r}. This is derived from the equation E×2πrl=λlϵ0E \times 2\pi r l = \frac{\lambda l}{\epsilon_0}, leading to E=λ2πϵ0rE = \frac{\lambda}{2\pi\epsilon_0 r}.

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