A closely wound solenoid of \(2000 \) turns and area of cross-section \(1.6 × 10^{-4}\ m^2\), carrying a current of \(4.0 \ A\), is suspended through its centre allowing it to turn in a horizontal plane.
(a) What is the magnetic moment associated with the solenoid?
(b) What is the force and torque on the solenoid if a uniform horizontal magnetic field of \(7.5 × 10^{-2}\ T\) is set up at an angle of \(30º\) with the axis of the solenoid?
(a) What is the magnetic moment associated with the solenoid?
(b) What is the force and torque on the solenoid if a uniform horizontal magnetic field of \(7.5 × 10^{-2}\ T\) is set up at an angle of \(30º\) with the axis of the solenoid?
Approach Solution - 1
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.
Approach Solution -2
(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 \(= 0.048\ Nm^2\)
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Concepts Used:
Magnetism & Matter
Magnets are used in many devices like electric bells, telephones, radio, loudspeakers, motors, fans, screwdrivers, lifting heavy iron loads, super-fast trains, especially in foreign countries, refrigerators, etc.
Magnetite is the world’s first magnet. This is also called a natural magnet. Though magnets occur naturally, we can also impart magnetic properties to a substance. It would be an artificial magnet in that case.
Read More: Magnetism and Matter
Some of the properties of the magnetic field lines are:
- The lines and continuous and outside the magnet, the field lines originate from the North pole and terminate at the South pole
- They form closed loops traversing inside the magnet.
- But here the lines seem to originate from the South pole and terminate at the North pole to form closed loops.
- More number of close lines indicate a stronger magnetic field
- The lines do not intersect each other
- The tangent drawn at the field line gives the direction of the field at that point.