Question

Two small charged spheres A and B have charges of $10\text{μC}$ and $40\text{μC}$ respectively and are held at a separation of $90\text{cm}$ from each other. At what distance from A, electric field intensity would be zero?

• A. $22.5\text{cm}$
• B. $18\text{cm}$
• C. $30\text{cm}$
• D. $36\text{cm}$

Answer 1

The correct option is C

$30\text{cm}$

Step 1: Given data

$$\begin{gathered} q_A=10\mathrm{\mu C} \\ {q}_B=40\mathrm{\mu C} \\ L=90\mathrm{cm} \end{gathered}$$

Here,

$q_A$ is the charge of sphere A.

$q_B$ is the charge of the sphere B.

$L$ is the distance between sphere A and sphere B.

Step 2: Formula used

Electric field intensity

1. The electric field intensity would be zero when the electric field due to A will be equal to the electric field due to B.
2. Consider at a distance $x$ from sphere A , the electric field intensity will be equal.
3. The equation for the electric field intensity can be written as follows:

$$\begin{gathered} \frac{k{q}_A}{x^2}=\frac{k{q}_B}{{\left(L-\mathrm{x}\right)}^2} \\ \frac{q_A}{q_B}=\frac{x^2}{{\left(90\mathrm{cm}-\mathrm{x}\right)}^2} \end{gathered}$$

Here, $k$ is the constant.

Step 3: Calculation

The distance can be determined by substituting the charges in the equation as follows:

$$\begin{gathered} \frac{10\text{μC}}{40\text{μC}}=\frac{x^2}{{\left(90\mathrm{cm}-x\right)}^2} \\ \frac{1}{2}=\frac{x}{90\mathrm{cm}-x} \\ 3x=90\mathrm{cm} \\ x=30\text{cm} \end{gathered}$$

Hence, the distance from A is $30\text{cm}$.

Therefore, option (C) is correct.