Question:
If an infinitely long uniformly charged wire produces an electric field of intensity $E$ at a distance $d$ from it, then the linear charge density $\lambda$ of the wire is
If an infinitely long uniformly charged wire produces an electric field of intensity $E$ at a distance $d$ from it, then the linear charge density $\lambda$ of the wire is
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For infinite line charge:
- $E = \frac{\lambda}{2\pi \varepsilon_0 r}$
- Always remember cylindrical symmetry
Updated On: Apr 30, 2026
- $\pi \varepsilon_0 Ed$
- $\frac{\pi}{2}\varepsilon_0 Ed$
- $\frac{1}{2}\varepsilon_0 Ed$
- $2\pi \varepsilon_0 Ed$
- $\varepsilon_0 Ed$
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Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Concept:
Electric field due to an infinite line charge:
\[
E = \frac{\lambda}{2\pi \varepsilon_0 r}
\]
Step 1: Substitute $r = d$.
\[ E = \frac{\lambda}{2\pi \varepsilon_0 d} \]
Step 2: Solve for $\lambda$.
\[ \lambda = 2\pi \varepsilon_0 Ed \]
Step 1: Substitute $r = d$.
\[ E = \frac{\lambda}{2\pi \varepsilon_0 d} \]
Step 2: Solve for $\lambda$.
\[ \lambda = 2\pi \varepsilon_0 Ed \]
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