NEET Magnetic Effects of Current and Magnetism — Set 13

Question 1

A circular coil of radius $ 0.12 \, \text{m} $ with 35 turns carries $ 1.5 \, \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 35 \times 1.5}{2 \times 0.12} = \frac{21 \pi \times 10^{-6}}{0.24} = 8.75 \pi \times 10^{-5} \approx 2.75 \times 10^{-4} \, \text{T} $.

Question 2

A proton moves with a speed of $ 2 \times 10^6 \, \text{m/s} $ perpendicular to a uniform magnetic field of $ 0.5 \, \text{T} $. What is the radius of its circular path? (Mass of proton = $ 1.67 \times 10^{-27} \, \text{kg} $, charge = $ 1.6 \times 10^{-19} \, \text{C} $)

Accepted Answer

Radius $ r = \frac{mv}{qB} $. Substitute: $ r = \frac{1.67 \times 10^{-27} \times 2 \times 10^6}{1.6 \times 10^{-19} \times 0.5} = \frac{3.34 \times 10^{-21}}{8 \times 10^{-20}} = 4.175 \times 10^{-2} \, \text{m} = 4.18 \, \text{cm} $.

Question 3

A circular coil of 70 turns and radius $ 7 \, \text{cm} $ carries a current of $ 0.8 \, \text{A} $. What is the magnetic field at its center? ($ \mu_0 = 4 \pi \times 10^{-7} \, \text{T m/A} $)

Accepted Answer

Magnetic field $ B = \frac{\mu_0 N I}{2 R} $. $ B = \frac{4 \pi \times 10^{-7} \times 70 \times 0.8}{2 \times 0.07} = \frac{22.4 \pi \times 10^{-6}}{0.14} = 1.6 \pi \times 10^{-4} \approx 5.03 \times 10^{-4} \, \text{T} $.

NEET Physics: Magnetic Effects of Current and Magnetism — Practice Set 13

Q1. A circular coil of radius \( 0.12 \, \text{m} \) with 35 turns carries \( 1.5 \, \text{A} \). What is the magnetic field at the center? (\( \mu_0 = 4 \pi \times 10^{-7} \, \text{T m/A} \))

Q2. A proton moves with a speed of \( 2 \times 10^6 \, \text{m/s} \) perpendicular to a uniform magnetic field of \( 0.5 \, \text{T} \). What is the radius of its circular path? (Mass of proton = \( 1.67 \times 10^{-27} \, \text{kg} \), charge = \( 1.6 \times 10^{-19} \, \text{C} \))

Q3. A circular coil of 70 turns and radius \( 7 \, \text{cm} \) carries a current of \( 0.8 \, \text{A} \). What is the magnetic field at its center? (\( \mu_0 = 4 \pi \times 10^{-7} \, \text{T m/A} \))

Q4. A wire of length \( 1.5 \, \text{m} \) carrying \( 8 \, \text{A} \) is at \( 60^\circ \) to a magnetic field of \( 0.5 \, \text{T} \). What is the force on the wire?

Q5. A circular loop of radius \( 0.13 \, \text{m} \) with 20 turns carries a current of \( 3.5 \, \text{A} \). What is the magnetic field at the center? (\( \mu_0 = 4 \pi \times 10^{-7} \, \text{T m/A} \))

Q6. Which factor does not affect the magnetic field produced by a current element according to the Biot-Savart law?

Q7. An electron moves with a speed of \( 2 \times 10^6 \, \text{m/s} \) perpendicular to a magnetic field of \( 0.7 \, \text{T} \). What is the radius of its path? (Mass = \( 9.1 \times 10^{-31} \, \text{kg} \), charge = \( 1.6 \times 10^{-19} \, \text{C} \))

Q8. A long wire carries \( 12 \, \text{A} \). At what distance is the magnetic field \( 2.4 \times 10^{-6} \, \text{T} \)? (\( \mu_0 = 4 \pi \times 10^{-7} \, \text{T m/A} \))

Q9. A circular loop of radius \( 0.15 \, \text{m} \) with 15 turns carries a current of \( 2 \, \text{A} \). What is the magnetic field at the center? (\( \mu_0 = 4 \pi \times 10^{-7} \, \text{T m/A} \))

Q10. What happens to the torque on a rectangular current loop if the magnetic field direction is reversed?