Number of turns on the solenoid, n = 2000
Area of cross-section of the solenoid, A = 1.6 × 10-4 m2
Current in the solenoid, \(I\) = 4 A
a. The magnetic moment along the axis of the solenoid is calculated as:
M = nA \(I\)
= 2000 × 1.6 × 10-4 × 4
= 1.28 Am2
b. Magnetic field, B = 7.5 × 10-2 T
Angle between the magnetic field and the axis of the solenoid, \(\theta\) = \( 30\degree\)
Torque, τ = \(MB\sin\theta\)
=1.28 × 7.5 × 10-2 \(\sin30\degree\)
= 4.8 × 10-2 Nm
Since the magnetic field is uniform, the force on the solenoid is zero. The torque on the solenoid is 4.8 × 10-2 Nm.
(a) Associated magnetic moment,
\(μ_m = niA\)
\(μ_m = 2000 × 4 ×1.6 × 10^{-4}\) \(Am^2\)
\(μ_m = 1.28\ Am^2\)
(b) Toeque \(= μ_m B sin \theta\)
Toeque \(= 1.28 ×7.5 ×10^{-2} × sin 30^o\)
Toeque \(= 0.048\ Nm^2\)
Column I | Column II |
(1) | (P) Diamagnetic |
(2) | (Q) Paramagnetic |
(3) | (R) Ferromagnetic |
(4) | (S) Antiferromagnetic |
A proton is projected with speed v in magnetic field B of magnitude 1 T. The angle between velocity and magnetic field is 600 as shown below. The kinetic energy of a proton is 2 eV (mass of proton = \(1.67\times10^{-27} kg\), e = \(1.6\times10^{-19}\)C). The pitch of the path of the proton is approximately?
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