c) Change in angle between magnetic field and area only
d) Change in the magnetic field, area, or angle between them
Answer: d
Explanation: emf=-dϕ/dt. We know ϕ flux is the dot product of the magnetic field vector and area vector.
ϕ=BAcos(θ), hence if either of the three, that is, magnetic field, area, or angle changes, the emf will change, flux changes due to which emf can be induced.
Question: What happens to the current in a coil while accelerating a magnet inside it?
a) Increases
b) Decreases
c) Remains constant
d) Reverses
Answer: a
Explanation: A change in the magnetic field induces an emf. When there is an emf, there has to be current. Hence, when the magnet is moved inside a coil, the current in it increases.
Question: What is the consequence of motor effect?
a) Current
b) Voltage
c) Electromagnetic induction
d) EMF
Answer: c
Explanation: Motor effect is when a current carrying conductor in a magnetic field experiences a force, hence its consequence is electromagnetic induction.
Question: The formula for induced emf if magnetic field, length, and velocity of conductor all are mutually perpendicular is … .
a) emf=B²l
b) emf=Bil
c) emf=Blv
d) emf=B²v
Answer: c
Explanation: The formula for induced emf is emf=Blv, where B is the magnetic field, l is the length of the conductor, and v is the velocity with which it is moving in the magnetic field, and all three quantities are mutually perpendicular to each other.
Question: If a conductor 0.2m long moves with a velocity of 0.3m/s in a magnetic field of 5T, calculate the emf induced if the magnetic field, velocity, and length of conductor are mutually perpendicular to each other.
a) 0.3V
b) 0.03V
c) 30V
d) 3V
Answer: a
Explanation: The formula for induced emf is: emf=Blv if B, l, v are perpendicular to each other. Substituting the values of B, l, and v from the question, we get emf=0.3V.
Question: Find the length of a conductor which is moving with a velocity 0.4m/s in a magnetic field of 8T, inducing an emf of 20V if magnetic field, velocity, and length of conductor are mutually perpendicular to each other.
a) 50m
b) 5m
c) 6.25m
d) 0.5m
Answer: c
Explanation: The formula for induced emf is: emf=Blv if B, l, v are perpendicular to each other. Substituting the values of B, emf, and v from the question, we get l=6.25m.
Question: Find the strength of the magnetic field in a conductor 0.5m long moving with a velocity of 10m/s, inducing an emf of 20V if magnetic field, velocity, and length of conductor are mutually perpendicular to each other.
a) 1T
b) 2T
c) 3T
d) 4T
Answer: d
Explanation: The formula for induced emf is: emf=Blv if B, l, v are perpendicular to each other. Substituting the values of l, emf, and v from the question, we get B=4T.
Answer: b
Explanation: Electromotive force is not actually a force. It is basically a voltage. It is the voltage developed by any source of electrical energy.
Answer: c
Explanation: The SI unit of magnetic flux is weber (Wb). One weber is the flux produced when a uniform magnetic field of one tesla acts normally over an area of 1 cm2.
Question: Calculate the magnetic flux when the magnetic field is perpendicular to the surface area.
a) Minimum
b) Maximum
c) Zero
d) Depends on the surface area
Answer: b
Explanation: Magnetic flux = B A cos 0°
Magnetic flux = B A.
It follows that magnetic flux linked with a surface is maximum when the direction of the magnetic field is perpendicular to the surface area.
Question: Which type of physical quantity is magnetic flux?
a) Scalar
b) Vector
c) Isotropic
d) Isentropic
Answer: a
Explanation: The magnetic flux is measured as the product of the component of the magnetic field normal to the surface and the surface area. Magnetic flux is a scalar quantity.
Question: What is the instrument used in Faraday’s experiment?
a) Galvanometer
b) Ammeter
c) Voltmeter
d) Meter Bridge
Answer: a
Explanation: Faraday used a galvanometer and connected it to a coil. A bar magnet was pushed towards the coil, such that the north-pole is pointing towards the coil. As the bar magnet is shifted, the pointer in the galvanometer gets deflected, thus indicating the presence of current in the coil.
Question: Which among the following affects the deflection in the galvanometer?
a) Area of the coil
b) Current passing through the coil
c) Speed with which the bar magnet is pulled towards or away from the coil
d) Resistance offered for current flow
Answer: c
Explanation: The deflection of the pointer is larger or smaller depending upon the speed with which the bar magnet is pulled towards or away from the coil. Moreover, the direction of deflection of the pointer depends upon the direction of motion of the bar magnet.
Question: Which among the following is true about Faraday’s law of Induction?
a) An emf is induced in a conductor when it cuts the magnetic flux
b) An emf is induced in a conductor when it moves parallel to the magnetic field
c) An emf is induced in a conductor when it moves perpendicular to the magnetic field
d) An emf is induced in a conductor when it is just entering a magnetic field
Answer: a
Explanation: According to Faraday’s law of electromagnetic induction, an emf is induced in a conductor when it cuts across the flux of a magnetic field. If the two ends of the conductor are connected to an outside circuit, the induced emf causes current to flow in the circuit.
Question: What is proportional to the magnitude of the induced emf in the circuit?
a) Rate of change of current in the circuit
b) Rate of change of resistance offered
c) Rate of change of magnetic flux
d) Rate of change of voltage
Answer: c
Explanation: The magnitude of induced emf is equal is equal to the time rate of change of magnetic flux. It is mathematically expressed as: ε = dϕ / dt. The negative sign indicates the direction of the emf induced. This is Faraday’s second law of electromagnetic induction.
Question: Faraday’s laws are the result of the conservation of which quantity?
a) Momentum
b) Energy
c) Charge
d) Magnetic field
Answer: b
Explanation: Faraday’s laws are the result of the conservation of energy. These laws are based on the conversion of electrical energy into mechanical energy. Mechanical energy can be converted into electrical energy such as in the example of a dynamo. In the same way, electrical energy can be converted into mechanical energy such as in the example of an electric motor. Both of the above examples work on the principle of Faraday’s law.
Question: The magnetic flux in a closed circuit of resistance 20 Ω varies with time t as Φ = 4t³ + 2t² – 15t + 3. Calculate the magnitude of induced emf at t = 1s.
a) 3 V
b) 4 V
c) 5 V
d) 6 V
Answer: 1 V
Explanation:
To calculate the magnitude of the induced electromotive force (emf) at \(t = 1s\), we can use Faraday's law of electromagnetic induction, which relates the emf (\(ε\)) to the rate of change of magnetic flux (\(\frac{dΦ}{dt}\)) in a closed circuit:
$$
ε = -\frac{dΦ}{dt}
$$
Here, Φ is given as a function of time \(t\): \(Φ = 4t^3 + 2t^2 - 15t + 3\). So, we need to find \(\frac{dΦ}{dt}\) and then calculate the emf (\(ε\)) at \(t = 1s\).
Question: Which law is used in finding the direction of current in a.c. generator?
a) Maxwell’s law
b) Lenz’s law
c) Corkscrew law
d) Ampere circuital law
Answer: b
Explanation: In an a.c. generator, induced current due to a change of magnetic flux linked with a closed circuit can be found out using Lenz's law. Lenz's law, in electromagnetism, statement that an induced electric current flows in a direction such that the current opposes the change that induced it.
Identify the expression for the motional electromotive force from the following?
a) E = -vLB
b) E = vLB
c) E = v/LB
d) E = LB/v
Answer: a
Explanation: Motional electromotive is the emf induced by the motion of the conductor across the magnetic field. The expression for motional electromotive force is given by:
E = -vLB
This equation is true as long as the velocity, magnetic field, and length are mutually perpendicular to each other. The negative sign is associated with Lenz’s law.
A bar of length 0.7 m slides along metal rails at a speed of 1 m/s. The bar and rails are in a magnetic field of 20 T, pointing out into the page. Calculate the motional emf.
a) 0.7 V
b) 7 V
c) 14 V
d) 1.4 V
Answer: c
Explanation: Explanation: Length (L) = 0.7 m; Speed (v) = 1 m/s; Magnetic field (B) = 20 T
The required equation E = -vLB (The negative sign only applies to the direction)
E = 1 × 0.7 × 20
E = 0.7 × 20
E = 14 V
Therefore, the motional emf in the bar and rails is 14 V.
A bar of length 0.15 m slides along metal rails at a speed of 5 m/s. The bar and rails are in a magnetic field of 40 T, pointing out into the page. The resistance of two resistors in parallel is both 20 Ω, and the resistance of the bar is 5 Ω. What is the current in the bar?
a) 1 A
b) 2 A
c) 3 A
d) 5 A
Answer: b
Explanation: \(L = 0.15 m; B = 40 T; v = 5 m/s; R_1 = 10 Ω; R_2 = 10 Ω; R_3 = 5 Ω\)
Emf (E) = vLB = 5 × 0.15 × 40
E = 5 × 6
E = 30 V
R1 and R2 are in parallel ➔ \(\frac{1}{R} = \frac{1}{R_1} + \frac{1}{R_2} = \frac{1}{20} + \frac{1}{20} = \frac{2}{20} = \frac{1}{10}
\) ➔ R = 10 Ω
RTOT = R + R3 = 10 + 5 = 15 Ω
Therefore, current (I) = \(\frac{E}{R}\)
I = \(\frac{30}{15}\)
I = 2 A
A metal rod is forced to move with constant velocity along two parallel metal rails, connected with a strip of metal at one end across a magnetic field (B) of 0.5 T, pointing out of the page. The rod is of length 45 cm and the speed of the rod is 70 cm/s. The rod has a resistance of 10 Ω and the resistance of the rails and connector is negligible. What is the rate at which energy is being transferred to thermal energy?
a) 0.225 W
b) 22.55 W
c) 2.25 × \(10^{-4}\) W
d) 2.25 × \(10^{-3}\) W
Answer: d
Explanation:
Given:
\(B = 0.5 \, T\)
\(v = 70 \, cm/s = 70 \times 10^{-2} \, m/s\)
\(L = 45 \, cm = 45 \times 10^{-2} \, m\)
\(R = 10 \, Ω\)
Motional emf (\(E\)) can be calculated using \(E = vLB\):
$$
E = 70 \times 10^{-2} \times 45 \times 10^{-2} \times 0.5 = 0.15 \, V
$$
Now, calculate the current (\(I\)) using \(I = \frac{E}{R}\):
$$
I = \frac{0.15}{10} = 0.015 \, A
$$
The rate at which energy is being transferred to thermal energy (\(P\)) can be calculated using \(P = I^2R\):
$$
P = (0.015)^2 \times 10 = 2.25 \times 10^{-3} \, W
$$
Therefore, the rate at which energy is being transferred to thermal energy is \(2.25 \times 10^{-3} \, W\), which corresponds to option (d) in the given choices.