NEET Magnetic Effects of Current and Magnetism — Set 6

Question 1

A circular coil of radius $ 0.05 \, \text{m} $ with 30 turns carries $ 2.5 \, \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 30 \times 2.5}{2 \times 0.05} = \frac{30 \pi \times 10^{-6}}{0.1} = 3 \pi \times 10^{-4} \approx 9.42 \times 10^{-4} \, \text{T} $.

Question 2

A long wire carries $ 20 \, \text{A} $. At what distance from the wire is the magnetic field $ 4 \times 10^{-6} \, \text{T} $? ($ \mu_0 = 4 \pi \times 10^{-7} \, \text{T m/A} $)

Accepted Answer

$ B = \frac{\mu_0 I}{2 \pi r} $, so $ r = \frac{\mu_0 I}{2 \pi B} $. $ r = \frac{4 \pi \times 10^{-7} \times 20}{2 \pi \times 4 \times 10^{-6}} = \frac{8 \times 10^{-6}}{8 \times 10^{-6}} = 1 \, \text{m} $.

Question 3

A proton moves at $ 3 \times 10^7 \, \text{m/s} $ perpendicular to a field of $ 0.1 \, \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

$ r = \frac{mv}{qB} $. $ r = \frac{1.67 \times 10^{-27} \times 3 \times 10^7}{1.6 \times 10^{-19} \times 0.1} = \frac{5.01 \times 10^{-20}}{1.6 \times 10^{-20}} = 3.13125 \, \text{m} \approx 3.13 \, \text{m} $.

NEET Physics: Magnetic Effects of Current and Magnetism — Practice Set 6

Q1. A circular coil of radius \( 0.05 \, \text{m} \) with 30 turns carries \( 2.5 \, \text{A} \). What is the magnetic field at the center? (\( \mu_0 = 4 \pi \times 10^{-7} \, \text{T m/A} \))

Q2. A long wire carries \( 20 \, \text{A} \). At what distance from the wire is the magnetic field \( 4 \times 10^{-6} \, \text{T} \)? (\( \mu_0 = 4 \pi \times 10^{-7} \, \text{T m/A} \))

Q3. A proton moves at \( 3 \times 10^7 \, \text{m/s} \) perpendicular to a field of \( 0.1 \, \text{T} \). 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 straight wire of length \( 0.7 \, \text{m} \) carries a current of \( 5 \, \text{A} \) perpendicular to a uniform magnetic field of \( 0.6 \, \text{T} \). What is the force on the wire?

Q5. A square loop of side \( 0.2 \, \text{m} \) with 30 turns carries \( 1.5 \, \text{A} \) in a magnetic field of \( 0.4 \, \text{T} \). The plane of the loop is at \( 60^\circ \) to the field. What is the torque?

Q6. A long straight wire carries a current of \( 28 \, \text{A} \). What is the magnetic field at a distance of \( 0.35 \, \text{m} \) from it? (\( \mu_0 = 4 \pi \times 10^{-7} \, \text{T m/A} \))

Q7. Which rule is used to determine the direction of the magnetic field produced by a current-carrying straight wire?

Q8. A rectangular loop of area \( 0.05 \, \text{m}^2 \) with 16 turns carries \( 2.2 \, \text{A} \) in a field of \( 0.7 \, \text{T} \) at \( 45^\circ \) to the plane. What is the torque?

Q9. A wire of length \( 2 \, \text{m} \) carries a current of \( 5 \, \text{A} \) and is placed perpendicular to a magnetic field of \( 0.4 \, \text{T} \). What is the magnitude of the force on the wire?

Q10. A proton moves at \( 6 \times 10^7 \, \text{m/s} \) perpendicular to a field of \( 0.1 \, \text{T} \). What is the magnetic force? (Charge = \( 1.6 \times 10^{-19} \, \text{C} \))