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physics A-Level Physics
 
Solved problems for the chapter:
 

Magnetic Fields due to Currents

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Torque of a Magnetic Force
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Detailed solution steps are available at:
 
https://en.openprof.com/wb/chapter:magnetic_fields_due_to_currents/4480/


Example 1.

A bar magnet, which is suspended on a thin thread, is placed in a homogeneous magnetic field with a strength of 0.4 T in such a way that the thread is fixed in the centre of gravity, and the magnet is oriented horizontally. Calculate the magnetic moment of the magnet if the rotation of the magnet horizontally through an angle requires a torque of and the magnetic field lines are directed horizontally.

    
Example 2.

A wire is formed into a loop in the shape of a circle with a radius of 15 cm and placed in a homogeneous magnetic field with a density of 0.8 T so that the lines of the magnetic field do not pierce its plane. Calculate the torque with which the magnetic field tries to rotate the loop if a current of 9 A is passed through the wire.

    
3.

A loop, in the shape of a rectangle with sides 5 cm and 20 cm, is placed in a homogeneous magnetic field with a density of 0.5 T. Calculate the torque acting on the loop if it makes an angle with the direction of the magnetic field forces, and a current of 10 A flows through it.

    
4.

A circular loop with a radius of 15 cm is placed in a homogeneous magnetic field with a density of 1 T. We attach the loop to an axis that is perpendicular to the lines of the magnetic field so that the lines of the magnetic field do not pierce its plane. At the same time, a torsion spring with a torsion constant of 0.4 N m is attached to the axle. Calculate the current through the loop if it (together with the spring) is rotated by .

    
5.

A cylindrical coil with 400 turns and a base surface radius of 1 cm is placed in a homogeneous magnetic field with a density of 1 T. Calculate the maximum possible torque of the magnetic field on the coil if a current of 8 A is passed through the coil.

    
6.

A coil with a cross-sectional area of and 200 turns is placed in a homogeneous magnetic field with a density of 0.06 T. The magnetic field lines are oriented horizontally and perpendicularly to the coil. A 20 cm long rod, which has a body of mass 8 g suspended at the end, is placed in the coil. The coil can rotate around an axis where the axis is horizontal and perpendicular to the magnetic field lines (the axis is routed so that the weight can affect its rotation - see picture). Calculate the current through the coil if the coil is to rest in a horizontal position.


Equal torques of magnetic force and gravitational force

    
7.

In the space inside a larger coil, there is a smaller coil, which is positioned so that its axis is perpendicular to the axis of the larger coil. The length of the larger coil is 40 cm, and the number of turns of the wire is 200. The smaller coil has 60 turns, a cross-sectional area of , and a current of 2 A flows through it.

How much torque acts on the smaller coil after passing through the larger coil which has an electric current of 5 A flowing through it? What position is the torque trying to put the smaller coil into?