NEET Magnetic Effects of Current and Magnetism — Set 4

Question 1

A circular coil of radius $ 0.06 \, \text{m} $ with 25 turns carries $ 3 \, \text{A} $. What is the magnetic field at the center? ($ \mu_0 = 4 \pi \times 10^{-7} \, \text{T m/A} $)

Accepted Answer

$ B = \frac{\mu_0 N I}{2 R} $. $ B = \frac{4 \pi \times 10^{-7} \times 25 \times 3}{2 \times 0.06} = \frac{30 \pi \times 10^{-6}}{0.12} = 2.5 \pi \times 10^{-4} \approx 7.85 \times 10^{-4} \, \text{T} $.

Question 2

A rectangular loop of area $ 0.06 \, \text{m}^2 $ with 22 turns carries $ 3 \, \text{A} $ in a field of $ 0.5 \, \text{T} $ perpendicular to the plane. What is the torque?

Accepted Answer

$ \tau = N I A B \sin \theta $, $ \theta = 90^\circ $ to plane means $ \sin 0^\circ = 1 $ with normal. $ \tau = 22 \times 3 \times 0.06 \times 0.5 \times 1 = 1.98 \, \text{N m} $.

Question 3

A proton moves with a speed of $ 5 \times 10^6 \, \text{m/s} $ perpendicular to a magnetic field of $ 0.4 \, \text{T} $. What is the radius of its path? (Mass = $ 1.67 \times 10^{-27} \, \text{kg} $, charge = $ 1.6 \times 10^{-19} \, \text{C} $)

Accepted Answer

Radius $ r = \frac{mv}{qB} $. $ r = \frac{1.67 \times 10^{-27} \times 5 \times 10^6}{1.6 \times 10^{-19} \times 0.4} = \frac{8.35 \times 10^{-21}}{6.4 \times 10^{-20}} = 1.3047 \times 10^{-1} \, \text{m} = 13.05 \, \text{cm} $.

NEET Physics: Magnetic Effects of Current and Magnetism — Practice Set 4

Q1. A circular coil of radius \( 0.06 \, \text{m} \) with 25 turns carries \( 3 \, \text{A} \). What is the magnetic field at the center? (\( \mu_0 = 4 \pi \times 10^{-7} \, \text{T m/A} \))

Q2. A rectangular loop of area \( 0.06 \, \text{m}^2 \) with 22 turns carries \( 3 \, \text{A} \) in a field of \( 0.5 \, \text{T} \) perpendicular to the plane. What is the torque?

Q3. A proton moves with a speed of \( 5 \times 10^6 \, \text{m/s} \) perpendicular to a magnetic field of \( 0.4 \, \text{T} \). What is the radius of its path? (Mass = \( 1.67 \times 10^{-27} \, \text{kg} \), charge = \( 1.6 \times 10^{-19} \, \text{C} \))

Q4. A long wire carries \( 24 \, \text{A} \). At what distance is the magnetic field \( 4.8 \times 10^{-6} \, \text{T} \)? (\( \mu_0 = 4 \pi \times 10^{-7} \, \text{T m/A} \))

Q5. Two parallel wires \( 0.05 \, \text{m} \) apart carry currents of \( 6 \, \text{A} \) and \( 4 \, \text{A} \) in the same direction. What is the force per unit length between them? (\( \mu_0 = 4 \pi \times 10^{-7} \, \text{T m/A} \))

Q6. An electron moves with a speed of \( 3.5 \times 10^6 \, \text{m/s} \) perpendicular to a magnetic field of \( 0.25 \, \text{T} \). What is the radius of its path? (Mass = \( 9.1 \times 10^{-31} \, \text{kg} \), charge = \( 1.6 \times 10^{-19} \, \text{C} \))

Q7. Why do parallel currents attract each other?

Q8. A circular coil of 55 turns and radius \( 3 \, \text{cm} \) carries a current of \( 1.5 \, \text{A} \). What is the magnetic field at its center? (\( \mu_0 = 4 \pi \times 10^{-7} \, \text{T m/A} \))

Q9. A rectangular loop of area \( 0.03 \, \text{m}^2 \) with 20 turns carries \( 2 \, \text{A} \) in a field of \( 0.7 \, \text{T} \) at \( 45^\circ \) to the plane. What is the torque?

Q10. A straight wire of length \( 1.1 \, \text{m} \) carries a current of \( 4 \, \text{A} \) perpendicular to a uniform magnetic field of \( 0.3 \, \text{T} \). What is the force on the wire?