Question

The electric potential at a certain distance from a point charge is $600V$ and the electric field is $200N/C$. Which of the following statements will be true?

• A. The work done in moving a point charge of $1\mu C$ from the given point to a point at a distance of$9m$ will be $4\times {10}^{-4}$
• B. The distance of the given point from the charge is $3m$
• C. The potential at a distance of $9m$ will be $200V$
• D. The magnitude of the charge is $2\times {10}^{-3}C$

Answer 1

Answer: (A), (B), (C)

The potential at a distance of $9m$ will be $200V$

Step 1: Given Data

The electric field at that point is, $E=200N/C$

The electric potential at that point is, $V=600V$

Step 2: Formula Used

Electric field, $E=\frac{1}{4\pi {\epsilon }_0}\frac{Q}{r^2}$

Electric potential, $V=\frac{1}{4\pi {\epsilon }_0}\frac{Q}{r}$

Work done in moving a charge $q$ from $r_1$to $r_2$ is $W=\frac{Qq}{4\pi {\epsilon }_0}(\frac{1}{r_2}-\frac{1}{r_1})$

Step 3: Calculation for the distance of the point from the charge

Using the formula, $E=\frac{V}{r}$

Substituting the values ⇒ $200=\frac{600}{r}$

⇒ The distance of the point from the charge is $r=3m$

Step 4: Calculating magnitude of the charge

Given, $V=600V=\frac{1}{4\pi {\epsilon }_0}\frac{Q}{r}$

⇒ $600=9\times {10}^9\frac{Q}{3}$

⇒ The value of the charge is, $Q=2\times {10}^{-7}C$

Step 5: Calculation for work done

Work done in moving charge of $1\mu C$ from $3m$ to $9m$ is $W=-\frac{2\times {10}^{-7}\times 1\times {10}^{-6}}{4\pi {\epsilon }_0}(\frac{1}{3}-\frac{1}{9})$

⇒ $W=-4\times {10}^{-4}J$

⇒ The magnitude of work done is = $4\times {10}^{-4}J$

Step 6: Finding the potential at a distance $9m$

Potential at a distance of $9m$ from the point is, $V=\frac{1}{4\pi {\epsilon }_0}\frac{2\times {10}^{-7}}{9}$

⇒ $V=200V$

⇒ The potential at a distance of $9m$ is = $200V$.

Hence, the correct options are (A), (B) and (C).