Question

The electric field due to an infinitely long line of charge at a point is $10\text{N/C}$. What is the electric field magnitude at a point which is twice as far from the line of charge?

• A. $20\text{N/C}$
• B. $5\text{N/C}$
• C. $1\text{N/C}$
• D. $2.5\text{N/C}$

Answer 1

The correct option is B

$5\text{N/C}$

The electric field due to an infinitely long line of charge is inversely proportional to the perpendicular distance from the line of charge. It varies as $\frac{\lambda }{4\pi {\epsilon }_{0}r}$ where $r$ is the perpendicular distance from the line of charge.

Now, as the distance becomes twice, the electric field will drop to half as there is an inverse relation.
Therefore, Electric field at this new point will be $5\text{N/C}$