(MCQ) The correct mathematical formula for magnetic flux ($\Phi_B$) over an area $\vec{A}$ in a uniform magnetic field $\vec{B}$ is:
(a) $\vec{B} \times \vec{A}$
(b) $\frac{\vec{B}}{\vec{A}}$
(c) $\vec{B} \cdot \vec{A}$
(d) $B + A$
3.
(MCQ) Faraday’s Law states that the magnitude of induced EMF is directly proportional to the:
(a) Magnetic flux
(b) Resistance of the coil
(c) Rate of change of magnetic flux
(d) Area of the coil
4.
(Fill in the blank) The phenomenon of generating electric current by changing magnetic fields is known as Electromagnetic ____________.
5.
(Fill in the blank) 1 Weber is equal to 1 Tesla multiplied by 1 ____________.
6.
(True/False) Magnetic flux is a vector quantity.
7.
(One Word) Who discovered electromagnetic induction independently in the USA at the same time as Michael Faraday in the UK?
8.
(One Word) What is the widely used CGS unit of magnetic flux?
9.
(Formula) Write the formula for induced EMF ($e$) for a coil of $N$ turns according to Faraday's law of induction.
10.
(MCQ) Magnetic flux linking a surface is maximum when the angle $\theta$ between the area vector and the magnetic field lines is:
(a) $90^\circ$
(b) $45^\circ$
(c) $180^\circ$
(d) $0^\circ$
Topic 6.2: Lenz’s Law
11.
(MCQ) Lenz’s Law is a direct consequence of the law of conservation of:
(a) Charge
(b) Momentum
(c) Energy
(d) Mass
12.
(MCQ) The negative sign in Faraday’s equation ($e = - \frac{d\Phi}{dt}$) is mathematically justified by:
(a) Ampere's Law
(b) Lenz's Law
(c) Gauss's Law
(d) Biot-Savart Law
13.
(MCQ) If the North pole of a bar magnet is brought rapidly near a closed conducting coil, the face of the coil facing the magnet will act as a:
(a) South pole
(b) North pole
(c) Positive charge
(d) Negative charge
14.
(Fill in the blank) According to Lenz's law, the induced current always flows in such a direction as to ____________ the change that produced it.
15.
(Fill in the blank) The mechanical work done in moving a magnet against the opposing force of an induced current is converted into ____________ energy.
16.
(True/False) Lenz's law is used strictly to determine the exact magnitude of the induced EMF.
17.
(True/False) If the inward magnetic flux into the plane of a closed loop is continuously decreasing, the induced current will flow in a clockwise direction.
18.
(One Word) Name the specific law that exclusively provides the direction of the induced EMF or current in a circuit.
19.
(MCQ) Which hand rule is sometimes used alternatively to find the direction of induced current in a straight conductor moving in a magnetic field?
(a) Fleming's Left-Hand Rule
(b) Fleming's Right-Hand Rule
(c) Maxwell's Corkscrew Rule
(d) Right-Hand Thumb Rule
20.
(One Word) Does Lenz's law violate the principle of conservation of energy? (Yes/No)
Topic 6.3: Motional EMF
21.
(MCQ) The motional EMF $E$ induced across the ends of a straight conducting rod of length $l$ moving with velocity $v$ perpendicularly to a uniform magnetic field $B$ is:
(a) $\frac{1}{2} B l v$
(b) $B^2 l v$
(c) $B l v$
(d) $\frac{B v}{l}$
22.
(MCQ) If a conducting rod of length $l$ rotates with angular velocity $\omega$ in a uniform perpendicular magnetic field $B$, the EMF induced between its center and one end is:
(a) $B \omega l$
(b) $\frac{1}{2} B \omega l^2$
(c) $B \omega l^2$
(d) $\frac{1}{2} B^2 \omega l$
23.
(MCQ) Motional EMF arises fundamentally due to the magnetic Lorentz force acting on the free ____________ inside the moving conductor.
(a) Protons
(b) Neutrons
(c) Electrons
(d) Atoms
24.
(Fill in the blank) The magnitude of the magnetic Lorentz force on an electron of charge $e$ moving with velocity $v$ perpendicular to field $B$ inside the rod is ____________.
25.
(Fill in the blank) To induce a steady motional EMF, the moving conductor must physically "cut" the magnetic ____________ lines.
26.
(True/False) If a straight conducting rod moves perfectly parallel to uniform magnetic field lines, the motional EMF induced across it is zero.
27.
(True/False) The value of the induced motional EMF depends on the electrical resistance of the rod.
28.
(Formula) Write the formula for the electrical power $P$ required to push a rod of length $l$ and resistance $R$ with constant velocity $v$ in a perpendicular field $B$.
29.
(Formula) Complete the vector scalar triple product formula for motional EMF: $E = \int (\vec{v} \times \vec{B}) \cdot d\vec{l}$. When $\vec{v}, \vec{B}, \vec{l}$ are mutually perpendicular, what does it simplify to?
30.
(MCQ) The induced EMF is maximum when a conductor moves:
(a) Parallel to the magnetic field
(b) At $45^\circ$ to the magnetic field
(c) Perpendicular to the magnetic field
(d) Anti-parallel to the magnetic field
Topic 6.4: Eddy Currents
31.
(MCQ) Eddy currents are induced primarily in:
(a) Thin conducting wires
(b) Insulating materials
(c) Bulk solid metallic blocks
(d) Semiconductors only
32.
(MCQ) The undesirable heating effect of eddy currents in transformers can be effectively minimized by using:
(a) Solid copper cores
(b) Laminated soft iron cores
(c) Thicker wires
(d) Higher voltages
33.
(MCQ) Which of the following is NOT a practical application of eddy currents?
(a) Magnetic braking in trains
(b) Induction furnaces
(c) Dead-beat galvanometers
(d) Electric room heaters (resistance wire)
34.
(Fill in the blank) Industrial induction furnaces utilize the intense heat generated by large ____________ currents to melt metal alloys.
35.
(Fill in the blank) The rapid stopping of a swinging copper pendulum plate as it enters a strong magnetic field is known as Electromagnetic ____________.
36.
(True/False) Eddy currents always dissipate energy by producing a Joule heating effect within the bulk conductor.
37.
(True/False) Large eddy currents are highly desirable and beneficial inside the iron core of an AC transformer.
38.
(One Word) What specific type of frictionless braking is used in some modern high-speed electric trains based on this principle?
39.
(One Word) What is the alternative name for Eddy Currents, named after the physicist who discovered them?
40.
(MCQ) Cutting long slots or holes in a metal plate swinging through a magnetic field will:
(a) Increase the eddy currents
(b) Reduce the eddy currents
(c) Have no effect at all
(d) Change the direction of gravity
Topic 6.5: Inductance
41.
(MCQ) The standard SI unit of self-inductance and mutual inductance is the:
(a) Faraday
(b) Henry
(c) Weber
(d) Tesla
42.
(MCQ) The self-inductance ($L$) of an ideal long air-cored solenoid of length $l$, area $A$, and $N$ total turns is:
(a) $\frac{\mu_0 N^2 A}{l}$
(b) $\frac{\mu_0 N A}{l}$
(c) $\mu_0 N^2 A l$
(d) $\frac{\mu_0 N A^2}{l}$
43.
(MCQ) The phenomenon by which an opposing EMF is induced in a coil strictly due to the changing current in the same coil is called:
(a) Mutual induction
(b) Self-induction
(c) Electromagnetic damping
(d) Capacitance
44.
(Fill in the blank) The mutual inductance ($M$) between two adjacent coils depends strongly on their relative geometry and ____________ to each other.
45.
(Fill in the blank) Because it physically opposes any growth or decay of current, Self-inductance is often referred to as the electrical analogue of mechanical ____________.
46.
(True/False) The unit Henry (H) is dimensionally equivalent to Weber per Ampere (Wb/A).
47.
(True/False) Inserting a ferromagnetic soft iron core inside a solenoid will dramatically decrease its self-inductance.
48.
(One Word) What is the generic name of the passive electrical circuit component specifically designed to introduce self-inductance?
49.
(Formula) Write the formula for the magnetic potential energy ($U$) stored in an inductor of inductance $L$ carrying a steady current $I$.
50.
(Formula) Write the formula for the Mutual Inductance ($M$) of two long perfectly coaxial solenoids of length $l$, inner cross-sectional area $A$, and turn densities $n_1$ and $n_2$.
Topic 6.6: AC Generator
51.
(MCQ) An AC Generator acts as a machine that systematically converts:
(a) Electrical energy into mechanical energy
(b) Chemical energy into electrical energy
(c) Mechanical energy into electrical energy
(d) Heat energy into mechanical energy
52.
(MCQ) The fundamental working principle of an AC generator is:
(a) Heating effect of current
(b) Magnetic effect of current
(c) Electromagnetic Induction
(d) Lorentz force on stationary charges
53.
(MCQ) The peak (maximum) induced EMF ($E_0$) generated by an AC generator coil rotating with angular velocity $\omega$ is given by:
(a) $NAB$
(b) $NAB\omega$
(c) $\frac{NAB}{\omega}$
(d) $N^2 AB\omega$
54.
(Fill in the blank) In an AC generator setup, the ends of the rotating armature coil are smoothly connected to the external stationary circuit via two continuous slip ____________.
55.
(Fill in the blank) The induced EMF essentially alternates its polarity because the angle ($\theta$) between the coil's area vector and the magnetic field changes ____________ with time.
56.
(True/False) The AC voltage frequency ($Hz$) in the external circuit is exactly equal to the frequency of physical rotation of the armature coil inside the generator.
57.
(True/False) A split ring commutator (half-rings) is an essential component used to maintain the alternating nature of the current in an AC generator.
58.
(One Word) What is the technical name for the main rotating coil assembly inside a generator or motor?
59.
(Formula) Write the sine-wave expression for the instantaneous EMF $e(t)$ produced by an AC generator at any time $t$.
60.
(One Word) In the generator formula $E_0 = NAB\omega$, what specific physical quantity does $\omega$ strictly represent?
