Advertisements
Advertisements
प्रश्न
Derive the expression for the torque on a rectangular current carrying loop suspended in a uniform magnetic field.
उत्तर
Consider a rectangular loop ABCD carrying current I.
Case I - The rectangular loop is placed such that the uniform magnetic field B is in the plane of loop.
No force is exerted by the magnetic field on the arms AD and BC.
Magnetic field exerts a force F1 on arm AB.
∴F1 = IbB
Magnetic field exerts a force F2 on arm CD.
∴F2 = IbB = F1
Net force on the loop is zero.
The torque on the loop rotates the loop in anti-clockwise direction.
Torque, τ = `f_1 a/2 + f_2 a/2`
`= IbBa/2 +IbBa/2`
= I(ab)B
τ = BIA
If there are ‘n’ such turns the torque will be nIAB
where, b → Breadth of the rectangular coil
a → Length of the rectangular coil
A = ab → Area of the coil
Case II - Plane of the loop is not along the magnetic field, but makes angle with it.
Angle between the field and the normal is θ.
Forces on BC and DA are equal and opposite and they cancel each other as they are collinear.
Force on AB is F1 and force on CD is F2.
F1 = F2 = IbB
Magnitude of torque on the loop as in the figure:
APPEARS IN
संबंधित प्रश्न
Two concentric circular coils X and Y of radii 16 cm and 10 cm, respectively, lie in the same vertical plane containing the north to south direction. Coil X has 20 turns and carries a current of 16 A; coil Y has 25 turns and carries a current of 18 A. The sense of the current in X is anticlockwise, and clockwise in Y, for an observer looking at the coils facing west. Give the magnitude and direction of the net magnetic field due to the coils at their centre.
At a place, the horizontal component of earth's magnetic field is B and angle of dip is 60°. What is the value of horizontal component of the earth's magnetic field at equator?
Two circular coils of radii 5.0 cm and 10 cm carry equal currents of 2.0 A. The coils have 50 and 100 turns respectively and are placed in such a way that their planes as well as the centres coincide. If the outer coil is rotated through 90° about a diameter, Find the magnitude of the magnetic field B at the common centre of the coils if the currents in the coils are (a) in the same sense (b) in the opposite sense.
A circular loop of radius 20 cm carries a current of 10 A. An electron crosses the plane of the loop with a speed of 2.0 × 106 m s−1. The direction of motion makes an angle of 30° with the axis of the circle and passes through its centre. Find the magnitude of the magnetic force on the electron at the instant it crosses the plane.
A circular loop of radius r carries a current i. How should a long, straight wire carrying a current 4i be placed in the plane of the circle so that the magnetic field at the centre becomes zero?
The magnitude of the magnetic field due to a circular coil of radius R carrying a current I at an axial distance x from the centre is ______.
A charged particle moving in a uniform magnetic field and losses 4% of its kinetic energy. The radius of curvature of its path changes by ______.
A small square loop of wire of side l is placed inside a large square loop of side L (L >> l). The loop is coplanar and their centers coincide. The mutual inductance of the system is proportional to is
An electron is projected along the axis of a circular conductor carrying some current. Electron ______
