Question

If a proton is displaced by 5m in an electric field of \(50 \, \text{N/C}\), what is the work done by the electric field?

Hint:

To find the work done by an electric field, multiply the force on the charge by the displacement in the direction of the force.

Answer 1

Step 1: Use the formula for work done by a force.
The work \(W\) done by the electric field is given by the formula: \[ W = F \times d \] where: - \( F \) is the force on the proton, and - \( d \) is the displacement.
Step 2: Calculate the force on the proton.
The force \(F\) on a charged particle in an electric field is given by: \[ F = q \times E \] where:
- \( q \) is the charge of the proton (\( q = 1.6 \times 10^{-19} \, \text{C} \)),
- \( E \) is the electric field strength (\( E = 50 \, \text{N/C} \)).
Thus, the force on the proton is: \[ F = (1.6 \times 10^{-19} \, \text{C}) \times (50 \, \text{N/C}) = 8 \times 10^{-18} \, \text{N} \]
Step 3: Calculate the work done.
Now, use the formula for work: \[ W = F \times d = (8 \times 10^{-18} \, \text{N}) \times 5 \, \text{m} = 4 \times 10^{-17} \, \text{J} \] Thus, the work done by the electric field is: \[ \boxed{4 \times 10^{-17} \, \text{J}} \]