Question

A positive point charge is placed at the origin. There is an electric field \( E'(x) = 2, 2 + 3 \) that accelerates the Udder point charge along the x-axis. Determine the energy of the charge when it reaches the position \( x = 21 \).

• A. \( 6 \, qdE_0 \)
• B. \( 12 \, q \)
• C. \( 12 \, qdE_0 \)
• D. \( 24 \, qdE_0 \)

Hint:

To find the energy, calculate the work done by the force along the distance traveled using the relationship \( W = F \cdot d \).

Answer 1

The Correct Option is C

The work done on a charge is given by the equation:

\[ W = F \cdot d = qE \cdot d \] where \( W \) is the work done, \( q \) is the charge, \( E \) is the electric field, and \( d \) is the displacement. Using the given electric field \( E_0 \), the work done is:

\[ W = q \cdot E_0 \cdot 12 \] Thus, the energy of the charge at \( x = 21 \) is given by \( 12qdE_0 \), where \( d \) is the displacement. This represents the total energy transferred to the charge as it moves in the electric field.

Hence, the correct answer is (c).