Question

The kinetic energy of a charged particle decreases by 10 joules as it moves from a point at potential 200 volt to a point at potential 250 volt. Find the charge on the particle.

Hint:

The work done in moving a charge in an electric field is equal to the change in the kinetic energy of the charge, and is related to the potential difference.

Answer 1

Step 1: Formula for Work Done in Moving a Charge in an Electric Field.
The work done \( W \) in moving a charge \( q \) through a potential difference \( \Delta V \) is given by: \[ W = q \Delta V \] Where:
- \( W = -10 \, \text{J} \) (since the kinetic energy decreases, the work done is negativ,
- \( \Delta V = V_{\text{final}} - V_{\text{initial}} = 250 \, \text{V} - 200 \, \text{V} = 50 \, \text{V} \).
Step 2: Substituting Known Values.
Substitute the given values into the equation: \[ -10 = q \times 50 \]
Step 3: Solving for the Charge.
Solving for \( q \): \[ q = \frac{-10}{50} = -0.2 \, \text{C} \]
Final Answer:
The charge on the particle is \( \boxed{-0.2 \, \text{C}} \).