Question

a rectangular coil is pulled away from fixed current carrying cable as shown in the figure. the current induced in the loop is

Answer 1

clockwise

Answer 2

To determine the direction of the induced current in the loop, we will apply Faraday's Law of Electromagnetic Induction and Lenz's Law.

1. Determine the direction of the magnetic field produced by the current-carrying cable: Assume the current I in the long straight cable flows upwards (as is typical for such diagrams unless specified otherwise, and consistent with the visual representation of the problem). Using the right-hand thumb rule (thumb in the direction of current, fingers curl in the direction of the magnetic field), the magnetic field lines to the right of the cable (where the rectangular coil is located) will be directed into the page.

2. Analyze the change in magnetic flux through the rectangular coil: The strength of the magnetic field produced by a long straight wire is given by $B = \frac{\mu_0 I}{2\pi r}$, where r is the perpendicular distance from the wire. As the rectangular coil is pulled away from the cable, its average distance r from the cable increases. Since $B \propto 1/r$, an increase in r means the magnetic field strength B passing through the coil decreases. Therefore, the magnetic flux ($\Phi_B = \int \vec{B} \cdot d\vec{A}$) directed into the page through the coil is decreasing.

3. Apply Lenz's Law: Lenz's Law states that the induced current will flow in a direction that opposes the change in magnetic flux that caused it.

   • The original flux is into the page.
   • This flux is decreasing.
   • To oppose this decrease, the induced current must create its own magnetic field that is also into the page, thereby trying to maintain the original flux.

4. Determine the direction of the induced current in the loop: Using the right-hand rule for a current loop (curl fingers in the direction of current, thumb points in the direction of the magnetic field inside the loop): To produce a magnetic field into the page, the current in the rectangular coil must flow in a clockwise direction.

Explanation of the Solution:

The current in the cable creates a magnetic field into the page through the coil. As the coil moves away, the magnetic field strength decreases, leading to a decrease in magnetic flux into the page. By Lenz's Law, the induced current opposes this decrease by creating its own magnetic field into the page. For a loop, a clockwise current produces a magnetic field into the page.