Question 1

Q1: A circular coil of wire consisting of 100 turns, each of radius 8.0 cm carries a current of 0.40 A. What is the magnitude of the magnetic field B at t...

Accepted Answer

The magnitude of the magnetic field at the centre of a circular coil with N turns is given by the formula: *B = (μ₀  N  I) / (2  R)* Where:    N = number of turns = 100    I = current = 0.40 A    R = radius of the coil = 8.0 cm = 0.08 m *   μ₀ = permeability of free space = 4π × 10⁻⁷ T m A⁻¹ Substit...

Question 2

Q10: Two moving coil meters, M₁ and M₂ have the following particulars: R₁ = 10 Ω, N₁ = 30, A₁ = 3.6 × 10⁻³ m², B₁ = 0.25 T R₂ = 14 Ω, N₂ = 42, A₂ = 1.8 × 1...

Accepted Answer

Let k be the spring constant for both meters. (a) Ratio of Current Sensitivity The current sensitivity (CS) of a moving coil galvanometer is defined as the deflection per unit current (φ/I). *CS = (N  A  B) / k For meter M₁: CS₁ = (N₁  A₁  B₁) / k For meter M₂: CS₂ = (N₂  A₂  B₂) / k The ratio of th...

Question 3

Q11: In a chamber, a uniform magnetic field of 6.5 G (1 G = 10⁻⁴ T) is maintained. An electron is shot into the field with a speed of 4.8 × 10⁶ m s⁻¹ norma...

Accepted Answer

Explanation of Circular Path When an electron enters a magnetic field normal to its direction of motion, it experiences a magnetic force given by the Lorentz force equation: F = q(v × B). 1.  Direction of Force: According to the vector cross product, the direction of this force is always perpendicul...

Question 4

Q12: In Exercise 4.11 obtain the frequency of revolution of the electron in its circular orbit. Does the answer depend on the speed of the electron? Explai...

Accepted Answer

Calculation of Frequency The frequency of revolution (ν) of a charged particle in a circular orbit within a magnetic field is also known as the cyclotron frequency. It is related to the angular frequency (ω) by ω = 2πν. The magnetic force provides the centripetal force: *e  v  B = (mₑ  v²) / r We kn...

Question 5

Q13: (a) A circular coil of 30 turns and radius 8.0 cm carrying a current of 6.0 A is suspended vertically in a uniform horizontal magnetic field of magnit...

Accepted Answer

(a) Calculation of Counter-Torque To prevent the coil from turning, a counter-torque must be applied that is equal in magnitude and opposite in direction to the magnetic torque (τ) acting on the coil. The magnitude of the magnetic torque is given by: *τ = N  I  A  B  sin(θ) Where:    N = number of t...

Question 6

Q2: A long straight wire carries a current of 35 A. What is the magnitude of the field B at a point 20 cm from the wire?

Accepted Answer

The magnitude of the magnetic field (B) at a distance (r) from a long straight wire carrying a current (I) is given by Ampere's circuital law: *B = (μ₀  I) / (2  π  r)* Where:    I = current = 35 A    r = distance from the wire = 20 cm = 0.20 m    μ₀ = permeability of free space = 4π × 10⁻⁷ T m A⁻¹...

Question 7

Q3: A long straight wire in the horizontal plane carries a current of 50 A in north to south direction. Give the magnitude and direction of B at a point 2...

Accepted Answer

Magnitude of the Magnetic Field The magnitude of the magnetic field (B) at a distance (r) from a long straight wire is given by: *B = (μ₀  I) / (2  π  r)* Where:    I = current = 50 A    r = distance from the wire = 2.5 m    μ₀ = permeability of free space = 4π × 10⁻⁷ T m A⁻¹ Substituting the values...

Question 8

Q4: A horizontal overhead power line carries a current of 90 A in east to west direction. What is the magnitude and direction of the magnetic field due to...

Accepted Answer

Magnitude of the Magnetic Field The magnitude of the magnetic field (B) at a distance (r) from a long straight wire is given by: *B = (μ₀  I) / (2  π  r)* Where:    I = current = 90 A    r = distance from the wire = 1.5 m    μ₀ = permeability of free space = 4π × 10⁻⁷ T m A⁻¹ Substituting the values...

Question 9

Q5: What is the magnitude of magnetic force per unit length on a wire carrying a current of 8 A and making an angle of 30° with the direction of a uniform...

Accepted Answer

The magnetic force (F) on a straight wire of length (l) carrying a current (I) in a uniform magnetic field (B) is given by: *F = I  l  B  sin(θ) Where θ is the angle between the direction of the current and the magnetic field. To find the force per unit length (f), we divide the force F by the lengt...

Question 10

Q6: A 3.0 cm wire carrying a current of 10 A is placed inside a solenoid perpendicular to its axis. The magnetic field inside the solenoid is given to be...

Accepted Answer

The magnetic force (F) on a straight wire of length (l) carrying a current (I) in a uniform magnetic field (B) is given by the formula: *F = I  l  B  sin(θ)* Where θ is the angle between the wire (direction of current) and the magnetic field. Given:    l = length of the wire = 3.0 cm = 0.03 m    I =...

Question 11

Q7: Two long and parallel straight wires A and B carrying currents of 8.0 A and 5.0 A in the same direction are separated by a distance of 4.0 cm. Estimat...

Accepted Answer

The force per unit length (f) between two long parallel wires is given by: *f = (μ₀  Iₐ  Iₑ) / (2  π  d) Where:    Iₐ = current in wire A = 8.0 A    Iₑ = current in wire B = 5.0 A    d = distance between the wires = 4.0 cm = 0.04 m    μ₀ = permeability of free space = 4π × 10⁻⁷ T m A⁻¹ First, we cal...

Question 12

Q8: A closely wound solenoid 80 cm long has 5 layers of windings of 400 turns each. The diameter of the solenoid is 1.8 cm. If the current carried is 8.0...

Accepted Answer

The magnitude of the magnetic field (B) inside a long solenoid near its centre is given by the formula: *B = μ₀  n  I Where:    μ₀ = permeability of free space = 4π × 10⁻⁷ T m A⁻¹    I = current = 8.0 A    n = number of turns per unit length First, we need to calculate 'n'.    Length of the solenoid...

Question 13

Q9: A square coil of side 10 cm consists of 20 turns and carries a current of 12 A. The coil is suspended vertically and the normal to the plane of the co...

Accepted Answer

The magnitude of the torque (τ) experienced by a current-carrying coil in a uniform magnetic field is given by: *τ = N  I  A  B  sin(θ) Where:    N = number of turns = 20    I = current = 12 A    A = area of the coil    B = magnitude of the magnetic field = 0.80 T    θ = angle between the normal to...

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