Question

Electric field intensity and electric potential at a point due to a point charge are 600 V/m and -3600 V respectively. The distance of the point from the charge and the magnitude of the charge are:

• A. \(7 \, {m}, 3 \, \mu{C}\)
• B. \(8 \, {m}, 4 \, \mu{C}\)
• C. \(6 \, {m}, 2.4 \, \mu{C}\)
• D. \(4 \, {m}, 6 \, \mu{C}\)

Hint:

For electrostatic problems involving a point charge, knowing either the electric field or potential at a distance can determine the other, along with the charge's magnitude and distance.

Answer 1

The Correct Option is C

Step 1: Use the formulas for electric field and potential. \[ E = \frac{kQ}{r^2} \] \[ V = \frac{kQ}{r} \] \[ E = \frac{V}{r} \] \[ 600 = \frac{3600}{r} \] \[ r = 6 \, {m} \] Step 2: Calculate the charge \(Q\). \[ Q = \frac{r^2 E}{k} \] \[ Q = \frac{6^2 \times 600}{9 \times 10^9} \] \[ Q = 2.4 \, \mu{C} \]

Answer 2

To solve the problem, we need to find the distance of the point from the charge and the magnitude of the charge based on the given electric field intensity and electric potential.

1. Given Data:
We are given:

• Electric field intensity \( E = 600 \, \text{V/m} \)
• Electric potential \( V = -3600 \, \text{V} \)

2. Formula for Electric Field and Potential:
For a point charge, the electric field intensity \( E \) and electric potential \( V \) are related to the charge \( q \) and the distance \( r \) as follows: \[ E = \frac{kq}{r^2} \] and \[ V = \frac{kq}{r} \] where \( k \) is Coulomb's constant \( k = 9 \times 10^9 \, \text{N m}^2/\text{C}^2 \).

3. Solving for the Distance \( r \):
From the equation for potential, we can solve for the distance \( r \): \[ r = \frac{kq}{V} \] Substituting the value of \( V = -3600 \, \text{V} \) into the equation gives the distance.

4. Solving for the Charge \( q \):
Now, we can substitute the value of \( r \) into the equation for the electric field \( E = \frac{kq}{r^2} \) to solve for the magnitude of the charge \( q \). This results in the values for the charge and distance of the point from the charge.

Final Answer:
The correct option is (C) \( r = 6 \, \text{m} \), \( q = 2.4 \, \mu\text{C} \).