Question

A square closed loop of area A, lying in the horizontal plane, is moving horizontally with velocity \( v \) in a uniform vertical magnetic field \( B \). Which one of the following statements is FALSE?

• A. There is current in the loop even though there is no battery (or any other voltage source)
• B. The work done in moving the coil is being converted to the current in the coil
• C. The current is being generated because the magnetic field is doing the work.
• D. The emf generated is proportional to the velocity of the coil
• E. The emf generated is proportional to the magnetic field strength

Hint:

In problems involving moving loops in a magnetic field, use Faraday’s Law to calculate induced emf and understand the role of motion, not the magnetic field alone.

Answer 1

The Correct Option is C

Statement Analysis:

a) There is current in the loop even though there is no battery (or any other voltage source)

True. According to Faraday's Law of Induction, a changing magnetic field induces an electromotive force (emf) in a conductor, and this emf generates an electric current. In this case, the moving square loop is subjected to a changing magnetic field as it moves, which induces the current in the loop, despite there being no external voltage source like a battery.

b) The work done in moving the coil is being converted to the current in the coil

True. The energy required to move the loop is converted into electrical energy in the form of the induced current. This is consistent with the law of conservation of energy: the mechanical work done in moving the coil is transformed into electrical energy in the circuit.

c) The current is being generated because the magnetic field is doing the work

False. The magnetic field does not perform work on the loop. The magnetic force on a moving charge is always perpendicular to the velocity of the charge, meaning it does no work (since work is the product of force and displacement in the direction of the force). Instead, the work comes from the mechanical effort used to move the loop through the magnetic field, which causes the induced emf and current.

d) The emf generated is proportional to the velocity of the coil

True. According to Faraday's Law of Induction, the induced emf in a conductor is proportional to the rate of change of magnetic flux. The magnetic flux changes when the loop moves through the magnetic field, and the rate of change of flux is proportional to the velocity at which the loop moves. Hence, the emf generated is indeed proportional to the velocity of the coil.

e) The emf generated is proportional to the magnetic field strength

False. The induced emf depends on the rate of change of magnetic flux, which is a product of both the velocity of the moving coil and the magnetic field strength. While the magnetic field strength does play a role, the emf is actually proportional to the velocity of the coil as well. It is the combination of both velocity and magnetic field strength that affects the induced emf, not just the magnetic field strength alone.

Conclusion:

The correct answers are (a), (b), and (d). The other statements are false based on the principles of electromagnetic induction.

Answer 2

Concept: 
When a loop moves in a magnetic field, an emf is induced due to Faraday's Law of Electromagnetic Induction, which states:

$$ \mathcal{E} = \frac{d\Phi}{dt} $$ Where $\Phi$ is the magnetic flux. If the magnetic field is uniform and perpendicular to the loop (vertical), and the loop moves horizontally, the flux through the loop remains constant because the area and field are unchanged and there's no change in orientation or cutting of magnetic field lines.

Thus, no emf is induced just by horizontal motion in a uniform vertical magnetic field.

Let’s analyze the options:

• (a) There is current in the loop even though there is no battery → FALSE (since no emf is induced)
• (b) The work done in moving the coil is being converted to the current in the coil → FALSE if no emf, so linked to (a)
• (c) The current is being generated because the magnetic field is doing the work → FALSE (magnetic field does no work)
• (d) The emf generated is proportional to the velocity of the coil → TRUE, in a changing flux case
• (e) The emf generated is proportional to the magnetic field strength → TRUE, again in changing flux scenario

Correct answer:
(c) The current is being generated because the magnetic field is doing the work.
Because magnetic fields do no work — the force due to a magnetic field is always perpendicular to velocity.

Answer 3

As the loop moves through the magnetic field, the changing magnetic flux through the loop induces an emf according to Faraday's Law. The work done in moving the coil is converted into electrical energy, but it is not the magnetic field doing the work. The current is generated due to the movement of the coil in the magnetic field. Thus, option (c) is false.