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A rectangular current carrying loop is placed in a uniform magnetic field of magnitude B. The angle between the plane perpendicular to the coil and the magnetic field is θ. The current in the loop is I. Then the torque on the rectangular loop will be-

A rectangular current carrying loop is placed in a uniform magnetic field of magnitude B. The angle between the plane perpendicular to the coil and the magnetic field is θ. The current in the loop is I. Then the torque on the rectangular loop will be- Correct Answer B I A sinθ

CONCEPT:

  • As the current-carrying conductor experiences a force when placed in a magnetic field, each side of a current-carrying rectangular coil experiences a force in a magnetic field.
  •  In the present section, we shall see in what way the rectangular loop carrying current is influenced by a magnetic field.

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  • Consider a rectangular coil of length l and breadth b carrying a current I placed in a uniform magnetic field B.
  • θ, be the angle between the plane of the rectangular coil and the magnetic field.


Force acting on the rectangular loop:

F = I L B sinθ, where F is force, I = current, L = distance from the axis, B = strength of the magnetic field, θ = angle between the plane of the rectangular coil and the magnetic field.

  • Acting on the upper and lower sides are equal and opposite along the same line of action, they cancel each other.
  • As the force acting on the sides QR and SP are equal and opposite along different lines of action they constitute a couple.


So, the torque acting on the loop is,

T = force × arm of the couple

T = B I L × b Sinθ = B I A Sinθ

T = B I A Sinθ

EXPLANATION:

  • The torque acting on the rectangular loop is


T = B I A sin θ.

So option 2 is correct.

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