Question

Which of the following graphs correctly represents the variation of $\overrightarrow{E}$ vs $r$ for two point charges $+q$ and $-2q$ kept some distance apart along the line joining these two charges?

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

$E-r$ graph


In region $\text{I}$

The electric field $E_1$ due to the charge $+q$ is towards left (so negative) and $E_2$ due to the charge $-2q$ is towards right (so positive).

Near the charge $+q$, electric field $E_1$ will dominate. So, net value will be negative.

At some point say $P$ both positive and negative values will become equal. So, $E_p=0$. Beyond this point, electric field due $E_2$ will dominate due to its higher magnitude. So, net value will be positive.

Then we will obtain a maximum value after which the value of the electric field will start decreasing until it reaches $0$.

In region $\text{II}$

$E_1$ due to $+q$ and $E_2$ due to $-2q$ are towards right (so positive). Near the charge, electric field manitude will be towards infinity.

In region $\text{III}$

$E_1$ due to $+q$ is towards right (so positive) and $E_2$ due to $-2q$ is towards left (so negative). But electric field $E_2$ of $-2q$ will dominate due to its higher magnitude and lesser distance. Hence, net electric field is always negative as shown.

Hence, option (a) is the correct answer.