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Right CHOICE is (d) F=IlB

The best explanation: The CURRENT passing through conductor in a perpendicular magnetic FIELD is GIVEN as:

I=\(\frac {\varepsilon}{r}\)

I=\(\frac {Blv}{r}\)

Since it is a perpendicular magnetic field, the FORCE ➔ I(l×B) is directed outwards in the direction opposite to the velocity of the rod. The magnitude of the force is given as:

F=IlB

We can also write it as ➔ F=IlB=\(\frac {B^2 l^2 v}{r}\)

The correct choice is (B) 2 A

Explanation: L = 0.15 m; B = 40 T; v = 5 m/s; R1 = 10 Ω; R2 = 10 Ω; R3 = 5 Ω

Emf (E) = vLB = 5 × 0.15 × 40

E = 5 × 6

E = 30 V

R1 and R2 are in parallel ➔ \(\frac {1}{R} = \frac {1}{R1} + \frac {1}{R2} = \frac {1}{20} + \frac {1}{20} = \frac {2}{20} = \frac {1}{10}\) ➔ R = 10 Ω

RTOT = R + R3 = 10 + 5 = 15 Ω

Therefore, CURRENT (I) = \(\frac {E}{R}\)

I = \(\frac {30}{15}\)

I = 2 A

The correct OPTION is (c) θ = 0^o

For explanation I would SAY: A normal to a plane can be drawn from either side. If the normal drawn to a plane points out in the DIRECTION of the field, then θ = 0^o and the flux are taken as positive. If the flux is positive and increasing the VOLTAGE will be negative.

The correct answer is (d) The permittivity of the core material

The explanation is: Self-inductance is DIRECTLY proportional to the number of TURNS and the area of cross-section. The self-inductance of a solenoid increases μr times if it is wound over an IRON core of relative PERMEABILITY μr.

Correct option is (a) Energy consideration PROVIDES a LINK between the force and energy

For EXPLANATION: Energy consideration provides a link the force and energy. NEWTON’s problems can also be easily solved with the help of energy consideration. This is the SIGNIFICANCE of energy consideration.

The correct choice is (a) Lenz’s law is a consequence of the law of conservation of energy

To elaborate: Whether a MAGNET is moved towards or away from a closed coil, the induced CURRENT ALWAYS opposes the motion of the magnet, as predicted by Lenz’s law. Work has to be DONE in MOVING the magnet closer to the coil against this force of repulsion. Thus Lenz’s law is valid and is a consequence of the law of conservation of energy.

Right ANSWER is (b) 4 V

Explanation: Given: RESISTANCE = 20 Ω; Φ = 4t^3 + 2t^2 – 15t + 3

Required equation ➔ ε = \(\FRAC {-dΦ}{dt}\)

ε=\(\frac {-d(4t^3 + 2t^2 – 15t + 3)}{dt}\) = -(12t^2 + 4t – 15t + 3)

= -12 – 4 + 15 – 3(Since t = 1s)

= 4 V

Therefore, the magnitude of induced EMF is 4V.

The correct choice is (c) Motional emf is directly PROPORTIONAL to the magnetic field

For explanation: Motional emf is directly proportional to the magnetic field across which the ELECTRIC CONDUCTOR moves. It is ALSO directly proportional to the \(\frac {velocity}{speed}\) of the electric conductor as well as to the LENGTH of the conductor. All the other statements are not valid.

Right answer is (b) False

For explanation: When a magnet is moved TOWARDS or away from a CLOSED coil, the induced current always opposes the MOTION of the magnet, as PREDICTED by Lenz’s law. Thus Lenz’s law is valid and is a consequence of the law of conservation of energy.

The correct answer is (a) Scalar

To explain: 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.

The correct CHOICE is (b) X ➔ BAR magnet; Y ➔ Current carrying coil

Explanation: In the second experiment, Faraday REPLACED the bar magnet by a second current carrying coil that was connected to a BATTERY. As we move the second coil towards the primary coil, the pointer in the galvanometer undergoes deflection, which INDICATES the presence of the electric current in the first coil.

Correct answer is (b) Lenz’s law

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.

The CORRECT answer is (a) An EMF is induced in a conductor when it CUTS the magnetic flux

The best I can explain: 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.

Right choice is (a) 1 × 10^-2 WB

The EXPLANATION is: Self-inductance = \(\frac {Magnetic \, flux}{Current}\)

Self-inductance = \(\frac {50 \times 10^{-3}}{5}\)

Self-inductance = 1 × 10^-2 Wb

The correct answer is (d) VsA^-1

The explanation is: Mutual INDUCTANCE is the interaction of one coils MAGNETIC field on another coil as it induces a voltage in the adjacent coil. UNIT of Mutual inductance = \(\frac {V}{As^{-1}}\).

SI unit = VsA^-1.

Right option is (a) Ammeter

To elaborate: Although eddy currents are UNDESIRABLE, still they find APPLICATIONS in the following DEVICES: Induction furnace, Electromagnetic damping, Electric BRAKES, Speedometers, Induction motor, Electromagnetic shielding, and ENERGY meters.

Correct answer is (B) 0.362

The best EXPLANATION: Given: N = 30; A = 3.14 × 10^-2 m^2 ; Angular velocity (ω) = 70 rad^-1; B = 5 × 10^-2 T; R = 15 Ω

Emf (E) = NABω

E = 30 × 3.14 × 10^-2 × 5 × 10^-2× 70

E = 3.297 V

Current (I) = \(\frac {E}{R}\)

I = \(\frac {3.297}{15}\)

I = 0.2198 A

Average power loss (P) = \(\frac {I^2 R}{2}\)

P = 0.2198^2 × \(\frac {15}{2}\)

P = 0.362 W

Therefore, the average power loss DUE to Joule heating is 0.362 W.

The correct option is (c) Winding the COIL on the aluminum frame

For explanation: The electromagnetic damping can be increased by winding the coil on a LIGHTER COPPER or aluminum frame. As the frame moves in the magnetic field, EDDY currents are SET up in the frame which resists the motion of the coil.

Right choice is (c) ∆Q = \(\frac {\triangle \Phi_B}{r}\)

EASY explanation: There is a RELATIONSHIP between the charge flow through the CIRCUIT and the change in the magnetic flux. ACCORDING to Faraday’s Law, the induced emf is given by:

|ε|=\( \frac {\triangle \Phi_B}{\triangle t}\)

But, |ε|=Ir=\(( \frac {\triangle Q}{\triangle t} ) \)r

Therefore, the relation is given by:

∆Q = \(\frac {\triangle \Phi_B}{r}\)

Correct answer is (d) Zero

Easiest explanation: The MAGNETIC lines of force due to CURRENT are parallel to the plane of the loop. The flux linked with the loop is zero. HENCE no current is induced in the loop.

The CORRECT option is (d) 1 Wb = 10^8 MAXWELL

The BEST EXPLANATION: 1 Wb = 1 T × 1 m^2

Wb = 10^4 G × 10^4 cm^2.

1 Wb = 10^8 Maxwell.

Right answer is (c) 2800 V

Explanation: Given: L = 2 m; B = 50 T;

The bar is said to be falling freely, so ➔ u = 0

According to Newton’s third equation ➔ v^2 – u^2 = 2gh

v^2 = 2gh; h = 40 m

v = \(\sqrt{(2 × 9.8 × 40)}\)

v = 28 m/s

Motional emf (E) = vLB

E = 28 × 2 × 50

E = 2800 V

Correct ANSWER is (b) False

To elaborate: No. they are not EXACTLY the same. According to Faraday’s Law, an induced emf is created whenever there’s a changing magnetic FLUX through a loop. If the changing emf is due to some kind motion of a CONDUCTOR in a magnetic field, then it would be called as motional emf.

The correct OPTION is (c) Rate of change of magnetic FLUX

Best 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 = \(\frac {-d\phi }{dt}\)

The negative sign indicates the direction of the emf induced. This is Faraday’s SECOND law of ELECTROMAGNETIC induction.

The correct answer is (c) The direction of induced EMF

For explanation I would say: Lenz’s law is a general law for determining the direction of induced emf and hence that of induced CURRENT in a CIRCUIT. Lenz’s law states that the direction of an induced emf will be such that if it were to cause a current to FLOW in a conductor in an external circuit, then that current would generate a field that would oppose the change that created it.

Right choice is (a) True

Easiest explanation: ACCORDING to Faraday’s first LAW, whenever the amount of magnetic flux LINKED with a circuit changes, an emf is induced in the circuit. This induced emf persists as long as he change in magnetic flux CONTINUES. Therefore, this is a true statement.

Correct option is (a) Maxwell

Explanation: The CGS UNIT of MAGNETIC flux is Maxwell (Mx). One Maxwell is the flux produced when a uniform magnetic FIELD of one GAUSS acts normally over an area of 1 cm^2.

The CORRECT answer is (a) LENZ’s LAW

The best I can explain: Eddy currents are the currents induced in solid masses when the magnetic flux threading through them changes. Eddy currents also OPPOSE the change in magnetic flux, so their direction is GIVEN by Lenz’s law.

The correct choice is (a) Lenz’s law

To explain: Eddy currents are the currents induced in solid metallic MASSES when the magnetic FLUX threading through them changes. Eddy currents also oppose the CHANGE in magnetic flux, so their DIRECTION is GIVEN Lenz’s law.

The CORRECT option is (b) Maximum

The best EXPLANATION: Magnetic flux = B ΔS COS 0^0

Magnetic flux = B ΔS.

It FOLLOWS that magnetic flux linked with a surface is maximum when the direction of the magnetic FIELD is perpendicular to the surface area.

The correct option is (a) The relative motion between the coils was not compulsory for the current in the PRIMARY to be generated

For explanation I would say: The relative motion between the coils was not REALLY NECESSARY for the current in the primary to be generated. In the third experiment, Faraday PLACED two STATIONARY coils and connected one of them to the galvanometer and the other to a battery, through a push button. As the button was pressed, the galvanometer in the other coil showed a deflection, indicating the presence of current in that coil. All the other statements are not valid.

The CORRECT choice is (B) False

To explain: The magnetic flux through any surface place in a magnetic field is the total number of magnetic lines of force crossing this surface normally. It is measured as the product of the COMPONENT of the magnetic field normal to the surface and the surface AREA.

Correct option is (a) GALVANOMETER

For EXPLANATION I would SAY: 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.

The correct CHOICE is (b) False

Explanation: Self-induction of a coil is that the property by which it tends to TAKE care of the magnetic flux LINKED with it and opposes any change within the flux by inducing a CURRENT in it. This is the reason why self-induction is named inertia of ELECTRICITY.

Correct choice is (c) 14 V

The best 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.

Right CHOICE is (c) Zero

The best I can EXPLAIN: MAGNETIC flux = B ΔS cos 90^o

Magnetic flux = 0.

It follows that magnetic flux LINKED with a surface is zero when the direction of the magnetic field is parallel to the surface area.

The correct option is (a) E = -vLB

The best I can EXPLAIN: 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.