Question

The electric field due to an infinitely long line of charge at a point is 10 N/c. What is the electric field magnitude at a point which is twice as far from the line of charge

• A. 20 N/c
• B. 5 N/c
• C. 1 N/c
• D. 2.5 N/c

Answer 1

The correct option is B

5 N/c

The electric field due to an infinitely long line of charge of uniform linear charge density varies with inverse of 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. [In any case, if you don’t know this as a fact please goes through the derivation video for an infinitely long line charge]

Now, as the distance becomes twice, the electric field will drop to half as there is a linear inverse relation