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Difficulty: MediumElectromagnetic Induction

A long straight conductor lying in the plane of the page carries a steady current directed towards the top of the page. A rectangular conducting loop lies in the same plane to the right of the conductor. If the loop is pulled horizontally to the right away from the conductor, what is the direction of the induced current in the loop and the direction of the net magnetic force exerted on the loop?

  1. Clockwise induced current and a net magnetic force directed to the left (towards the conductor)Answer
  2. B
    Counter-clockwise induced current and a net magnetic force directed to the right (away from the conductor)
  3. C
    Clockwise induced current and a net magnetic force directed to the right (away from the conductor)
  4. D
    Counter-clockwise induced current and a net magnetic force directed to the left (towards the conductor)

Answer

The induced current flows in a clockwise direction, and the net magnetic force acts to the left (towards the straight conductor).
The straight wire creates a magnetic field pointing into the page on its right side. Pulling the loop further away decreases the inward magnetic flux passing through it. By Lenz's law, the induced current must create an inward magnetic field to oppose this decrease, which corresponds to a clockwise current. Furthermore, Lenz's law requires the resulting mechanical magnetic force to oppose the rightward motion, producing a net force directed to the left (towards the conductor).

Step-by-Step Solution

1
Determine magnetic field direction around the long straight wire
Using the right-hand grip rule, the magnetic field B⃗\vec{B} produced by the upward current to the right of the wire points perpendicularly into the page.
Current flowing upward creates concentric magnetic field lines that enter the plane of the page on the right side.
2
Analyze magnetic flux change when moving the loop away
As the loop moves rightward away from the wire, it enters a region of weaker magnetic field, so magnetic flux pointing into the page decreases.
Magnetic field strength decreases inversely with distance (B∝1/rB \propto 1/r).
3
Apply Lenz's Law to find induced current direction
The induced current must oppose the decrease in magnetic flux into the page by producing its own magnetic field directed into the page. By the right-hand rule for loops, a clockwise current produces an inward field.
Lenz's law states that an induced current always flows in a direction such that its magnetic field opposes the change in magnetic flux causing it.
4
Determine the net magnetic force on the loop
According to Lenz's law, the net force must oppose the motion causing the induction. Since the loop moves right, the net force must point left (towards the conductor).
Alternatively, the left edge of the loop is closer to the wire and carries upward current (clockwise loop), parallel to the main wire's upward current. Parallel currents attract, yielding a net force to the left.

Key Concept

Lenz's Law and Electromagnetic Induction

Alternative Method

Consider magnetic forces on parallel current segments: The left side of the rectangular loop has current flowing upward (for clockwise flow), which is parallel to the main wire's upward current and is therefore attracted to the left. The right side has downward current (antiparallel) and is repelled to the right. Because the left side is closer to the wire, the attractive force dominates, yielding a net force to the left.
Estimated Time:1m 15s
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Topics

Electromagnetic Induction

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