Home
Class 12
PHYSICS
A length L of a wire carries a current I...

A length L of a wire carries a current I. Prove that if the wise is formed into a circular loop, the maximum torque in a given magnetic field will be developed if the coil has one turn only. Find the value of the maximum torque acting on the circular coil.

Text Solution

Verified by Experts

Let the circular coil formed has n turns each of radius r. Then `L=2pirn` or `r=L//2pin`
Area of the coil, `A=pir^2=(piL^2)/(4pi^2n^2)=(L^2)/(4pin^2)`
Torque on coil in magnetic field is
`tau=nIBA sin alpha=nIBxx(L^2)/(4pin^2)sinalpha`
`=(L^2IB)/(4pin)sin alpha`
Torque will be maximum if n is least `(=1)` and `sin alpha` has maximum value i.e., `sin alpha=1`
Thus torque will be maximum when `n=1`
Maximum value of Torque, `tau_(max.)=(L^2IB)/(4pi)`
Promotional Banner

Topper's Solved these Questions

  • MAGNETIC EFFECT OF CURRENT AND MAGNETISM

    PRADEEP|Exercise Conceptual Problems (d)|2 Videos

  • MAGNETIC EFFECT OF CURRENT AND MAGNETISM

    PRADEEP|Exercise Very Short Answer Questions (a)|2 Videos

  • ELECTROSTATICS

    PRADEEP|Exercise ASSERTION-REASON TYPE QUESTIONS|2 Videos

  • OPTICS

    PRADEEP|Exercise Multiple choice questions|1 Videos

Similar Questions

Explore conceptually related problems

A length L of wire carries a current i . Show that if the wire is formed into a circular coil, then the maximum torque in a given magnetic field is developed when the coil has one turn only, and that maximum torque has the magnitude tau=L^2iB/4pi

A length L of a wire carries a current I. Show that if the wire is formed into a circular coil, the maximum torque in a given magnetic fiel B, is developed when the coil has one turn only and the maximum torque has the value, tau_(max)=L^2IB//4pi .

Current i is carried in a wire of length L . If the wire is turned into a circular coil, the maximum magnitude of torque in a given magnetic field B will be

A wire of length l is formed into a circular loop of one turn only and is suspended in a magnetic field B. When a current i is passed through the loop, the maximum torque experienced by it is

A wire of length L is bent to form a circular loop of number of turns n. The coil is placed in a magnetic field of induction B and a current is passed through the coil. What will be the maximum torque acting on the coil?

For a given length l of wire carrying a current l, how many circular turns would produce the maximum magnetic moment ?

A rectangular coil of area vecA and number of turns n is placed in a uniform magnetic field vecB. If the coil carries a current I, then the torque acting on the coil is given by

A rectangular loop carrying a current i is placed in a uniform magnetic field B. The area enclosed by the loop is A. If there are n turns in the loop, the torque acting on the loop is given by