Q1: A wire carrying 4A current and has length of 15 cm between the poles of a magnet is kept at an angle of 30° to the uniform field of 0.8 T. Find the force acting on the wire?
Given:
Current, I = 4 A
Length, L = 15 cm = 0.15 m
Angle, θ = 30°
Magnetic field, B = 0.8 T
Formula: F = BIL sinθ
Calculation:
F = 0.8 × 4 × 0.15 × sin30°
sin30° = 0.5
F = 0.8 × 4 × 0.15 × 0.5
F = 0.8 × 4 × 0.075
F = 0.8 × 0.3
F = 0.24 N
Answer: 0.24 N
Current, I = 4 A
Length, L = 15 cm = 0.15 m
Angle, θ = 30°
Magnetic field, B = 0.8 T
Formula: F = BIL sinθ
Calculation:
F = 0.8 × 4 × 0.15 × sin30°
sin30° = 0.5
F = 0.8 × 4 × 0.15 × 0.5
F = 0.8 × 4 × 0.075
F = 0.8 × 0.3
F = 0.24 N
Answer: 0.24 N
Q2: A square loop of wire of side 2.0 cm carries 2.0 A of current. A uniform magnetic field of magnitude 0.7 T makes an angle of 30° with the plane of the loop. What is the magnitude of torque on the loop?
Given:
Side of square loop, a = 2.0 cm = 0.02 m
Area of loop, A = a² = (0.02)² = 4 × 10⁻⁴ m²
Current, I = 2.0 A
Magnetic field, B = 0.7 T
Angle with plane = 30°
Angle with normal, θ = 90° - 30° = 60°
Formula: τ = BIA sinθ
Calculation:
τ = 0.7 × 2.0 × (4 × 10⁻⁴) × sin60°
sin60° = 0.866
τ = 0.7 × 2.0 × 4 × 10⁻⁴ × 0.866
τ = 0.7 × 2.0 × 3.464 × 10⁻⁴
τ = 0.7 × 6.928 × 10⁻⁴
τ = 4.85 × 10⁻⁴ Nm
Answer: 4.85 × 10⁻⁴ Nm
Side of square loop, a = 2.0 cm = 0.02 m
Area of loop, A = a² = (0.02)² = 4 × 10⁻⁴ m²
Current, I = 2.0 A
Magnetic field, B = 0.7 T
Angle with plane = 30°
Angle with normal, θ = 90° - 30° = 60°
Formula: τ = BIA sinθ
Calculation:
τ = 0.7 × 2.0 × (4 × 10⁻⁴) × sin60°
sin60° = 0.866
τ = 0.7 × 2.0 × 4 × 10⁻⁴ × 0.866
τ = 0.7 × 2.0 × 3.464 × 10⁻⁴
τ = 0.7 × 6.928 × 10⁻⁴
τ = 4.85 × 10⁻⁴ Nm
Answer: 4.85 × 10⁻⁴ Nm
Q3: A transformer is needed to convert a mains 220 V supply into a 12 V supply. If there are 2200 turns on the primary coil, then find the number of turns on the secondary coil.
Given:
Primary voltage, Vₚ = 220 V
Secondary voltage, Vₛ = 12 V
Primary turns, Nₚ = 2200
Formula: Vₛ / Vₚ = Nₛ / Nₚ
Nₛ = (Vₛ / Vₚ) × Nₚ
Calculation:
Nₛ = (12 / 220) × 2200
Nₛ = (12 × 2200) / 220
Nₛ = 12 × 10
Nₛ = 120 turns
Answer: 120 turns
Primary voltage, Vₚ = 220 V
Secondary voltage, Vₛ = 12 V
Primary turns, Nₚ = 2200
Formula: Vₛ / Vₚ = Nₛ / Nₚ
Nₛ = (Vₛ / Vₚ) × Nₚ
Calculation:
Nₛ = (12 / 220) × 2200
Nₛ = (12 × 2200) / 220
Nₛ = 12 × 10
Nₛ = 120 turns
Answer: 120 turns
Q4: A coil surrounding a long solenoid, the current in the solenoid is changing at a rate of 150 A/s and the mutual induction of the two coils is 5.5 × 10⁻⁵ H. Determine the emf induced in the surrounding coil?
Given:
Rate of change of current, dI/dt = 150 A/s
Mutual inductance, M = 5.5 × 10⁻⁵ H
Formula: ε = -M (dI/dt)
Calculation:
ε = -(5.5 × 10⁻⁵) × 150
ε = -825 × 10⁻⁵
ε = -8.25 × 10⁻³ V
Answer: -8.25 × 10⁻³ V (negative sign indicates direction of induced emf)
Rate of change of current, dI/dt = 150 A/s
Mutual inductance, M = 5.5 × 10⁻⁵ H
Formula: ε = -M (dI/dt)
Calculation:
ε = -(5.5 × 10⁻⁵) × 150
ε = -825 × 10⁻⁵
ε = -8.25 × 10⁻³ V
Answer: -8.25 × 10⁻³ V (negative sign indicates direction of induced emf)
