Shrinking Loop. A circular loop of flexible iron wire has an initial circumference of 165.0 cm, but its circumference is decreasing at a constant rate of 12.0 cm/s due to a tangential pull on the wire. The loop is in a constant, uniform magnetic field oriented perpendicular to the plane of the loop and with magnitude 0.500 T. Find the direction of the induced current in the loop as viewed looking along the direction of the magnetic field.

검증된 단계별 안내

Understand that the problem involves electromagnetic induction, where a changing magnetic flux through a loop induces an electromotive force (EMF) and hence a current.

The loop's circumference is decreasing, which means its area is decreasing. Since the magnetic field is constant and perpendicular to the loop, the magnetic flux through the loop is decreasing.

According to Lenz's Law, the induced current will flow in a direction that opposes the change in magnetic flux. Since the flux is decreasing, the induced current will try to increase the flux.

The magnetic field is directed into the page (as indicated by the image with crosses), so the induced current must create a magnetic field in the same direction to oppose the decrease.

Using the right-hand rule, curl your fingers in the direction of the induced current such that your thumb points in the direction of the magnetic field (into the page). The fingers will curl clockwise, indicating the direction of the induced current is clockwise when viewed along the direction of the magnetic field.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Faraday's Law of Induction

Faraday's Law states that a change in magnetic flux through a loop induces an electromotive force (EMF) in the loop. The EMF is proportional to the rate of change of the magnetic flux. In this scenario, as the loop shrinks, the area decreases, leading to a change in magnetic flux, thus inducing a current.

Lenz's Law

Lenz's Law provides the direction of the induced current, stating that the induced current will flow in a direction that opposes the change in magnetic flux. As the loop shrinks, the magnetic flux decreases, so the induced current will flow to create a magnetic field that opposes this decrease, maintaining the original flux.

Right-Hand Rule

The Right-Hand Rule helps determine the direction of the induced current. When the thumb points in the direction of the magnetic field, the fingers curl in the direction of the induced current. In this case, looking along the direction of the magnetic field, the induced current will be counterclockwise to oppose the decrease in flux.