Advertisements
Advertisements
Question
Derive the expression for the torque acting on a current-carrying loop placed in a magnetic field.
Solution
The plane of the loop is not along the magnetic field but makes an angle with it.
Let the dimension of the rectangular coil ABCD, be AB × BC = a × b
The 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
The magnitude of the torque on the loop as in the figure:
`tau = F_1 a/2 sinθ + F_2 a/2 sinθ`
= IabBsinθ
If there are ‘n’ such turns the torque will be sin nIab sinθ
The magnetic moment of the current m = IA
`vectau = vecm xx vecB`
APPEARS IN
RELATED QUESTIONS
Draw a neat and labelled diagram of suspended coil type moving coil galvanometer.
Two very small identical circular loops, (1) and (2), carrying equal currents I are placed vertically (with respect to the plane of the paper) with their geometrical axes perpendicular to each other as shown in the figure. Find the magnitude and direction of the net magnetic field produced at the point O.
A circular loop of radius a, carrying a current i, is placed in a two-dimensional magnetic field. The centre of the loop coincides with the centre of the field (figure). The strength of the magnetic field at the periphery of the loop is B. Find the magnetic force on the wire.
A 50-turn circular coil of radius 2.0 cm carrying a current of 5.0 A is rotated in a magnetic field of strength 0.20 T. (a) What is the maximum torque that acts on the coil? (b) In a particular position of the coil, the torque acting on it is half of this maximum. What is the angle between the magnetic field and the plane of the coil?
A moving coil galvanometer has been fitted with a rectangular coil having 50 turns and dimensions 5 cm × 3 cm. The radial magnetic field in which the coil is suspended is of 0.05 Wb/m2. The torsional constant of the spring is 1.5 × 10−9 Nm/degree. Obtain the current required to be passed through the galvanometer so as to produce a deflection of 30°.
A 100 turn rectangular coil measuring 0.02 m x 0.06 m of an ammeter is in a magnetic field of induction 0.4 tesla. The torsional constant of the suspension fibre is 5 x 10-7 newton x metre/degree. The maximum reading of the ammeter corresponds to a deflection of the coil through 30°. If the magnetic field is radial, then the maximum current that can be measured with this ammeter is ____________.
A triangular loop of side `l` carries a current I. It is placed in a magnetic field B such that the plane of the loop is in the direction of B. The torque on the loop is ____________.
If in a moving coil galvanometer, a current I produces a deflection `theta,` then ____________.
A circular coil of 20 turns and radius 10 cm is placed in a uniform magnetic field of 0.10 T normal to the plane of the coil. If the current in the coil is 5.0 A, what is the
(a) total torque on the coil,
(b) total force on the coil,
(c) average force on each electron in the coil due to the magnetic field?
(The coil is made of copper wire of cross-sectional area 10–5 m2, and the free electron density in copper is given to be about 1029 m–3.)
A circular coil having N turns of radius R carrying a current I is used to produce a magnetic field B at its centre O.
If this coil is opened and rewound such that the radius of the newly formed coil is 2R, carrying the same current I, what will be the magnetic field at the centre O?
