Electromagnetic Induction

A coil of \(N\) turns and area \(A\) is placed in a uniform field \(B\). If \(B\) reduces uniformly to zero in time \(t\), the average emf induced is:

1. a\(\dfrac{N^{2}AB}{t}\)
2. b\(\dfrac{NAB}{t}\)
3. c\(\dfrac{NA^{2}B}{t}\)
4. d\(\dfrac{NB}{At}\)

A rod of length \(L\) moves with velocity \(v\) perpendicular to its length in a uniform field \(B\). The motional emf is:

1. a\(BL/v\)
2. b\(Bv/L\)
3. c\(BvL\)
4. d\(B^{2}vL\)

Self-inductance of a long solenoid of \(n\) turns/m, area \(A\) and length \(L\) is:

1. a\(\mu_{0} n L^{2} A\)
2. b\(\mu_{0} n A L\)
3. c\(\mu_{0} n^{2} A\)
4. d\(\mu_{0} n^{2} A L\)

Two coils have mutual inductance \(M = 0.2\ \text{H}\). The current in one changes from \(4\ \text{A}\) to 0 in \(0.1\ \text{s}\). The induced emf in the other coil is:

1. a\(2\ \text{V}\)
2. b\(8\ \text{V}\)
3. c\(0.4\ \text{V}\)
4. d\(20\ \text{V}\)

Energy stored in an inductor of inductance \(L\) carrying current \(I\) is:

1. a\(\tfrac{1}{2}\,L/I\)
2. b\(LI^{2}\)
3. c\(\tfrac{1}{2}LI^{2}\)
4. d\(L^{2}I/2\)

Lenz's law is a consequence of:

1. aconservation of charge
2. bconservation of energy
3. cconservation of momentum
4. dNewton's third law

A bar magnet is moved with its N-pole approaching a closed conducting loop. As seen from the magnet side, the induced current in the loop flows:

1. aclockwise
2. bzero
3. cfirst clockwise then reverses
4. danti-clockwise

Two concentric circular coils, a small one of radius \(r_{1}\) and a large one of radius \(r_{2}\) with \(r_{1} \ll r_{2}\), lie in the same plane with their centres coinciding. The mutual inductance of the arrangement is:

1. a\(\dfrac{\mu_{0}\pi r_{2}^{2}}{2r_{1}}\)
2. b\(\dfrac{\mu_{0}\pi r_{1}}{2r_{2}}\)
3. c\(\dfrac{\mu_{0}\pi r_{1}^{2}}{2r_{2}}\)
4. d\(\dfrac{\mu_{0} r_{1}^{2}}{2\pi r_{2}}\)

An AC generator of \(N\) turns, area \(A\), in field \(B\) rotates at angular speed \(\omega\). The peak emf is:

1. a\(NBA\omega\)
2. b\(BA\omega\)
3. c\(NBA\)
4. d\(NBA/\omega\)

Two long co-axial solenoids of the same length \(0.5\ \text{m}\) have \(1000\) and \(2000\) turns per metre. The inner one has radius \(2\ \text{cm}\). The mutual inductance of the pair is approximately:

1. a\(3.2\times10^{-3}\ \text{H}\)
2. b\(0.8\times10^{-3}\ \text{H}\)
3. c\(1.6\times10^{-3}\ \text{H}\)
4. d\(1.6\times10^{-2}\ \text{H}\)

Assertion (A): When a magnet is moved towards a closed conducting loop, the induced current in the loop opposes the motion of the magnet.

Reason (R): By Lenz's law, the direction of induced current is such that its magnetic field opposes the change in flux that produced it.

1. aBoth A and R are true, and R is the correct explanation for A
2. bBoth A and R are true, but R is NOT the correct explanation for A
3. cA is true, but R is false
4. dA is false, but R is true

Assertion (A): A uniform conducting wire is bent into a closed loop and placed in a region with a slowly increasing uniform magnetic field \(B\) perpendicular to the loop. The induced current is non-zero.

Reason (R): A changing magnetic flux through the loop induces an emf according to Faraday's law \(\varepsilon = -d\Phi/dt\).

1. aBoth A and R are true, and R is the correct explanation for A
2. bBoth A and R are true, but R is NOT the correct explanation for A
3. cA is true, but R is false
4. dA is false, but R is true

Assertion (A): If the space inside two long co-axial solenoids is filled with a material of relative permeability \(\mu_{r}\) (greater than 1), their mutual inductance stays the same as with air inside.

Reason (R): The mutual inductance of a pair of coils depends on their separation as well as on their relative orientation.

1. aBoth A and R are true, and R is the correct explanation for A
2. bBoth A and R are true, but R is NOT the correct explanation for A
3. cA is true, but R is false
4. dA is false, but R is true

Assertion (A): A rod moving in a uniform magnetic field experiences a motional emf even if there is no closed circuit.

Reason (R): In a moving conductor, free charges experience the Lorentz force \(q\vec{v}\times\vec{B}\), which separates positive and negative charges between the ends.

1. aBoth A and R are true, and R is the correct explanation for A
2. bBoth A and R are true, but R is NOT the correct explanation for A
3. cA is true, but R is false
4. dA is false, but R is true

1. I. The induced emf is proportional to the rate of change of magnetic flux.
2. II. An emf is induced even in an open conductor; only current requires a closed circuit.
3. III. The direction of induced emf is determined by Lenz's law.

Which of the above are CORRECT regarding Faraday's laws of electromagnetic induction?

1. aOnly I
2. bOnly I and II
3. cOnly II and III
4. dAll three

1. I. Self-inductance depends on the geometry of the coil.
2. II. Self-inductance depends on the permeability of the medium inside the coil.
3. III. An inductor opposes any change in current through it.

Which statements about self-inductance are CORRECT?

1. aOnly I
2. bAll three
3. cOnly II and III
4. dOnly I and II

1. I. Peak emf of an AC generator is \(\varepsilon_{0} = NBA\omega\).
2. II. The emf alternates sinusoidally with time.
3. III. Mechanical (rotational) energy is converted to electrical energy.

Which of the above are CORRECT for an AC generator?

1. aAll three
2. bOnly II
3. cOnly I and II
4. dOnly I

1. I. The self-induced emf in a coil of inductance \(L\) is \(\varepsilon = -L\,dI/dt\).
2. II. Energy stored in an inductor carrying steady current \(I\) is \(\tfrac{1}{2}LI^{2}\).

Which of the above CORRECTLY describe self-inductance of a coil?

1. aOnly I
2. bOnly II
3. cBoth I and II
4. dNeither

Match each item in List I with its corresponding entry in List II:

1. a(i)-S, (ii)-Q, (iii)-R, (iv)-P
2. b(i)-Q, (ii)-P, (iii)-S, (iv)-R
3. c(i)-R, (ii)-S, (iii)-P, (iv)-Q
4. d(i)-P, (ii)-Q, (iii)-R, (iv)-S

Match each item in List I with its corresponding entry in List II:

1. a(i)-Q, (ii)-P, (iii)-S, (iv)-R
2. b(i)-P, (ii)-Q, (iii)-R, (iv)-S
3. c(i)-R, (ii)-S, (iii)-P, (iv)-Q
4. d(i)-S, (ii)-Q, (iii)-R, (iv)-P

Match each item in List I with its corresponding entry in List II:

1. a(i)-R, (ii)-S, (iii)-P, (iv)-Q
2. b(i)-S, (ii)-R, (iii)-P, (iv)-Q
3. c(i)-R, (ii)-S, (iii)-Q, (iv)-P
4. d(i)-Q, (ii)-P, (iii)-R, (iv)-S

A \(5\ \text{mH}\) inductor carries a current that decreases linearly from \(4\ \text{A}\) to 0 in \(0.02\ \text{s}\). The magnitude of induced emf is:

1. a\(4.0\ \text{V}\)
2. b\(2.0\ \text{V}\)
3. c\(0.5\ \text{V}\)
4. d\(1.0\ \text{V}\)

A square loop of side \(10\ \text{cm}\) and resistance \(0.1\ \Omega\) is placed in a uniform field \(0.5\ \text{T}\) perpendicular to the plane of the loop. The field decreases uniformly to zero in \(0.1\ \text{s}\). The total charge that flows is:

1. a\(0.005\ \text{C}\)
2. b\(0.5\ \text{C}\)
3. c\(0.05\ \text{C}\)
4. d\(5.0\ \text{C}\)

An AC generator with peak emf \(220\ \text{V}\) and frequency \(50\ \text{Hz}\) has 100 turns of area \(0.01\ \text{m}^{2}\). The magnetic field is:

1. a\(220/\pi\ \text{T}\)
2. b\(0.7\ \text{T}\)
3. c\(7\ \text{T}\)
4. d\(2.2\ \text{T}\)

A circular loop lies in the plane of the page. A uniform magnetic field directed into the page increases steadily with time. As seen by the reader, the induced current in the loop is:

1. aclockwise
2. banticlockwise
3. czero
4. dalternating

A metal rod of length \(0.5\ \text{m}\) is rotated at 20 revolutions per second about an axis through one end and perpendicular to the rod, in a uniform magnetic field of \(0.2\ \text{T}\) parallel to the axis. The emf induced between the ends of the rod is approximately:

1. a\(6.28\ \text{V}\)
2. b\(1.57\ \text{V}\)
3. c\(0.5\ \text{V}\)
4. d\(3.14\ \text{V}\)

Based on the passage, the rate of change of flux through the loop is:

1. a\(Bav\)
2. b\(Ba/v\)
3. c\(Bv/a\)
4. d\(B/(av)\)

Based on the passage, the magnitude of induced emf is:

1. a\(B/(av)\)
2. b\(Bv/a\)
3. c\(Bav\)
4. d\(B^{2}av\)

Based on the passage, the force needed to keep the rod moving uniformly is:

1. a\(Bav\)
2. b\(\dfrac{Bav}{R}\)
3. c\(\dfrac{B^{2}a^{2}v}{R}\)
4. d\(\dfrac{B^{2}av^{2}}{R}\)

Based on the passage, the power dissipated as heat in the resistor equals:

1. a\(F\cdot v\)
2. b\(FvR\)
3. c\(F/v\)
4. dzero