Question

A square loop of side 15 cm being moved towards right at a constant speed of 2 cm/s as shown in figure. The front edge enters the 50 cm wide magnetic field at t = 0. The value of induced emf in the loop at t = 10 s will be :

• A. 0.3 mV
• B. 4.5 mV
• C. zero
• D. 3 mV

Answer 1

The Correct Option is C

To determine the induced EMF in the loop at \(t = 10 \text{ s}\), we can analyze the situation using the concept of electromagnetic induction. According to Faraday's law of electromagnetic induction, the EMF induced in a closed loop is equal to the negative rate of change of magnetic flux through the loop.

The formula for induced EMF \((\varepsilon)\) is given by:

\(\varepsilon = -\frac{{d\Phi}}{{dt}}\)

where \(\Phi\) is the magnetic flux.

Magnetic flux \((\Phi)\) through a coil is given by:

\(\Phi = B \times A\)

where \(B\) is the magnetic field strength and \(A\) is the area of the coil inside the magnetic field.

Initially, let's consider the position of the square loop:

• The loop is entering a magnetic field 50 cm in width.
• The loop has a side of 15 cm.

At \(t = 0\), the front edge of the loop just starts to enter the magnetic field.

At \(t = 10 \text{ s}\), the distance covered by the loop is:

\(d = \text{velocity} \times \text{time} = 2 \, \text{cm/s} \times 10 \, \text{s} = 20 \, \text{cm}\)

Since the loop has moved 20 cm and the side of the loop is 15 cm, the entire loop is now outside the magnetic field (since \(20 \, \text{cm} > 15 \, \text{cm} + 50 \, \text{cm}\)).

Therefore, since the loop is completely outside the magnetic field or has not yet fully entered it, the magnetic flux through the loop is zero.

Thus, the rate of change of magnetic flux \((\frac{d\Phi}{dt})\) is zero, and the induced EMF in the loop is:

\(\varepsilon = 0 \, \text{V}\)

Hence, the correct answer is zero EMF is induced in the loop.

Answer 2

At \( t = 10s \), the complete loop is already inside the magnetic field. Since the loop is entirely within the magnetic field, there is no change in the flux as the loop moves through the field. The rate of change of magnetic flux \( \frac{d\Phi}{dt} \) is zero because the area of the loop inside the magnetic field remains constant.

Thus, the induced emf is:

\( e = \frac{d\Phi}{dt} = 0. \)