Question

Two point charges q and 2q are placed some distance apart. If the electric field at the location of q be E, then that at the location of 2q will be
(a). 2E
(b). E/2
(c). E
(d). None of these

Answer 1

Hint: We can find the electric field at both the points where the charges are located due to each other. And then we can find the relation between the two values of the electric field by comparing the two values of electric fields we got.
Formula used:
Electric field due to a charge Q at a distance r from the charge is given by $E=\dfrac{kq}{r^2}$, where k is a constant with value $8.99\times 10^9\; Nm^2 /C^2$.

Complete step by step solution:
Let us consider the distance between the two charges q and 2q be d.

So, we know that electric field due to a charge Q at a distance r is given by the formula
$E=\dfrac{kQ}{r^2}$
Now, the electric field at charge 2q due to charge q will be, ${E}_{2q}=\dfrac{kq}{d^2}$
Similarly, electric field at charge q due to charge 2q will be, $E={E}_{q}=\dfrac{2kq}{d^2}$
Now, let us take the ratio of ${E}_{q}$ and ${E}_{2q}$,
Therefore, $\dfrac{{E}_{q}}{{E}_{2q}}=\dfrac{\dfrac{2kq}{d^2}}{\dfrac{kq}{d^2}}=2$
As, electric field at q is E, so $E={E}_{q}$
$\implies \dfrac{E}{{E}_{2q}}=2\implies {E}_{2q}=\dfrac{E}{2}$
Hence, option b is the correct answer.

Note: Mistake may happen while writing the formula for the electric field, that is on which charge the electric field is generated by which other charge.
We can also solve this question by using the formula of force due to a charge in an electric field as according to Newton’s third law, the forces on both the charges will be equal.