Now the switch on the electromagnet is reopened. The magnitude of the external magnetic flux through the wire loop _ (A. increases, B. decreases, C. remains constant), and there is __ (A. zero, B. a clockwise, C. a counterclockwise) current induced in the loop (as seen from the left.
The Correct Answer and Explanation is :
When the switch on the electromagnet is reopened, the external magnetic flux through the wire loop decreases, and a clockwise current is induced in the loop (as seen from the left). This phenomenon can be explained through the principles of electromagnetic induction, specifically Faraday’s Law and Lenz’s Law.
Faraday’s Law of Induction states that an electromotive force (emf) is induced in a circuit when there is a change in magnetic flux through the circuit. Mathematically, it is expressed as:
[ \mathcal{E} = -\frac{d\Phi_B}{dt} ]
where:
- ( \mathcal{E} ) is the induced emf
- ( \Phi_B ) is the magnetic flux
- ( \frac{d\Phi_B}{dt} ) is the rate of change of magnetic flux
Magnetic flux (( \Phi_B )) is the product of the magnetic field strength (( B )) and the area (( A )) through which the magnetic field lines pass, and the cosine of the angle (( \theta )) between the magnetic field and the normal to the surface:
[ \Phi_B = B \cdot A \cdot \cos(\theta) ]
When the electromagnet is turned off (i.e., the switch is reopened), the magnetic field strength ( B ) decreases, leading to a reduction in magnetic flux ( \Phi_B ) through the wire loop. According to Faraday’s Law, this change in magnetic flux induces an emf in the loop.
Lenz’s Law provides the direction of the induced current. It states that the direction of the induced current will be such that it opposes the change in magnetic flux that caused it. In this case, the decrease in magnetic flux through the loop is opposed by an induced current that creates a magnetic field attempting to maintain the original flux. To achieve this, the induced current must flow in a direction that produces a magnetic field pointing in the same direction as the original field.
To determine the direction of the induced current, we can use the right-hand rule. Point the thumb of your right hand in the direction of the magnetic field lines of the electromagnet (which is initially pointing into the page). The curl of your fingers around the loop shows the direction of the induced current. Since the magnetic field is decreasing, the induced current will flow in a direction that attempts to keep the magnetic flux constant, which, when viewed from the left, is clockwise.
In summary:
- The magnitude of the external magnetic flux through the wire loop decreases.
- A clockwise current is induced in the loop (as seen from the left).
This behavior aligns with the principles of electromagnetic induction, where a change in magnetic flux through a loop induces an emf and a current that opposes the change in flux.