Question

What is the angle between the current and the magnetic field if a conductor carrying 2A current placed in a magnetic field of 4T experiences a force of 10N?

• A. \( 90^\circ \)
• B. \( 45^\circ \)
• C. \( 30^\circ \)
• D. \( 60^\circ \)

Hint:

The maximum force on a current-carrying conductor in a magnetic field occurs when the angle between the current and the magnetic field is \( 90^\circ \).

Answer 1

The Correct Option is A

The force on a current-carrying conductor in a magnetic field is given by the formula: \[ F = BIL \sin \theta \] Where: - \( F \) is the force on the conductor, - \( B \) is the magnetic field strength, - \( I \) is the current in the conductor, - \( L \) is the length of the conductor in the magnetic field, - \( \theta \) is the angle between the magnetic field and the direction of current. We are given that: - \( F = 10 \, \text{N} \), - \( B = 4 \, \text{T} \), - \( I = 2 \, \text{A} \), - The angle \( \theta \) is unknown. Rearranging the formula to solve for \( \sin \theta \): \[ \sin \theta = \frac{F}{BIL} = \frac{10}{4 \times 2 \times L} \] Assuming that the length \( L \) of the conductor is such that the force is maximized, i.e., \( \sin \theta = 1 \), which implies \( \theta = 90^\circ \). Thus, the angle between the current and the magnetic field is \( 90^\circ \).