Question

An infinitely long thin straight wire a uniform linear charge density of $\frac{1}{3}C{m}^{-1}$. Then the magnitude of electric field intensity at a point $18cm$ away is $N{C}^{-1}$.

• A. $0.66\times {10}^{11}$
• B. $1.32\times {10}^{11}$
• C. $0.33\times {10}^{11}$
• D. $3\times {10}^{11}$

Answer 1

Answer: (C)

$0.33\times {10}^{11}$

An infinitely long thin straight wire is similar to a narrow long cylinder.

We know that for a cylinder $E=\frac{q}{2\pi ϵr}$

Where q is the linear charge density, and r is the distance of the point

From the above equation, $E=\frac{2q}{4\pi ϵr}=\frac{2\times 9\times {10}^9}{3\times 0.18}=\frac{2\times 9\times {10}^9\times {10}^2}{3\times 2\times 9}=0.33\times {10}^{11}N{C}^{-1}$