Faradays Laws Of Induction

Step 1: E=L(di)/(dt)
Step 2: (di)/(dt)=110⁻³=10³
Step 3: L=(4)/(10³)=4×10⁻³H

Step 1: Formula for induced emf. For a rotating rod: = (1)/(2) B ω l²
Step 2: Converting angular speed. ω = (2π × 1800)/(60) = 60π rad/s
Step 3: Substituting values. = (1)/(2) × 2.5×10⁻³ × 60π × 1² ≈ 0.471V

Step 1: Electromagnetic induction.
Electromagnetic induction refers to the process of generating electric current by changing magnetic fields. This principle is used in devices such as generators, which convert mechanical energy into electrical energy.
Thus, the correct answer is (4).

Step 1: Understand the concept of eddy currents.
Eddy currents are circular currents induced in a conductor when the magnetic field around it changes. These currents oppose the change in the magnetic flux according to Lenz's Law.
Step 2: Conclusion.
Eddy currents are produced when a metal is exposed to a varying magnetic field, causing changes in the magnetic flux through the metal. Final Answer:

Step 1: Use the formula for mutual inductance.
The mutual inductance of two coaxial solenoids is given by the formula: where and are the number of turns in the solenoids, is the cross-sectional area, is the length of the solenoids, and is the permeability of free space.
Step 2: Calculate the mutual inductance.
Substitute the given values to find the mutual inductance as . Final Answer:

Step 1: Change in magnetic flux:
Step 2:
Step 3: Induced charge: (Closest option is A)

Step 1: Magnetic flux through the loop:
Step 2: Induced emf:
Step 3: Since :

Step 1: Magnetic flux: Φ=BA=π Br²
Step 2: Induced emf: E=|(dΦ)/(dt)|=2π Br(dr)/(dt)
Step 3: Substituting values: E=2π(0.04)(0.02)(2×10⁻3) =4.8πμV

Step 1: Motion of the coil changes magnetic flux through the aluminium plate.
Step 2: Eddy currents are induced in the plate.
Step 3: These currents oppose the motion (Lenz’s law), causing damping.

Step 1: Time constant τ = (L)/(R) = (0.3)/(2) = 0.15s
Step 2: (I)/(I₀) = 1 - e⁻t/τ
Step 3: For I = (I₀)/(2): t = τ ln 2 ≈ 0.05s

Step 1: Motional emf in a rotating rod: E = int₀^ℓ Bω rdr
Step 2: E = Bω [(r²)/(2)]₀^ℓ = (1)/(2)Bω ℓ²

Step 1: Area of square loop: A = a²
Step 2: Rate of change of area: (dA)/(dt) = 2a(da)/(dt) = -2aα
Step 3: Induced emf: E = B|(dA)/(dt)| = 2α a B

Step 1: Magnetic flux through the loop: Φ = Bπ r²
Step 2: Induced emf: E = |(dΦ)/(dt)| = B · 2π r · |(dr)/(dt)|
Step 3: Substituting values: B=0.04T, r=2cm=0.02m, (dr)/(dt)=2mm/s=2×10⁻3m/s
Step 4: E =0.04× 2π × 0.02 × 2×10⁻3 ≈ 1.6×10⁻6V ⟹ E=1.6μV

Step 1: When the coil oscillates near the aluminium plate, the magnetic flux linked with the plate changes. Step 2: Changing magnetic flux induces eddy currents in the aluminium plate. Step 3: According to Lenz’s law, these eddy currents oppose the motion of the coil. Step 4: The opposing force causes electromagnetic damping, stopping the oscillations.