A wire of length l, carrying current is bent into a loop and placed with its plane perpendicular to a magnetic field. In which of the following shapes, is the torque acting on the loop maximum?a)Rectangleb)Circlec)Squared)Equilateral triangleCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

The torque on a current loop depends upon the area of the current loop, when the magnetic field is perpendicular to the plane of the loops the torque has its maximum value,
Τ=I A B
We know I and B for all these cases but A depends upon the geometry. The circle has the greatest area so it should provide the greatest torque.

Answer

Because in the given parameter circle have much greater area and we know that torque acting in magnetic field is dependent on area.

Answer

Bent Wire Loop in a Magnetic Field
When a wire carrying current is bent into a loop and placed in a magnetic field, a torque is exerted on the loop due to the interaction between the magnetic field and the current.

Torque on a Current Loop
The torque on a current loop in a magnetic field is given by the equation:
τ = NIA sinθ
where τ is the torque, N is the number of turns in the loop, I is the current flowing through the loop, A is the area of the loop, and θ is the angle between the magnetic field and the normal to the plane of the loop.

Effect of Shape on Torque
The torque acting on the loop depends on the shape of the loop and the orientation of the magnetic field with respect to the loop.

Rectangle
- In a rectangular loop, the torque is maximum when the magnetic field is parallel to one of the sides of the loop.
- The area vector of the loop is perpendicular to the plane of the loop, so the angle θ is 90 degrees.
- The torque in this case is given by τ = NIA.
- Therefore, the torque on a rectangular loop is proportional to the product of the number of turns, current, and the area of the loop.

Square
- A square is a special case of a rectangle, so the torque on a square loop will also be maximum when the magnetic field is parallel to one of the sides of the loop.
- The torque on a square loop is also given by τ = NIA.

Equilateral Triangle
- In an equilateral triangle, the torque is maximum when the magnetic field is parallel to one of the sides of the triangle.
- The area vector of the triangle is perpendicular to the plane of the triangle, so the angle θ is 90 degrees.
- The torque in this case is given by τ = (sqrt(3)/4)NIA.
- Therefore, the torque on an equilateral triangle is proportional to the product of the number of turns, current, and the area of the triangle, multiplied by a constant factor of (sqrt(3)/4).

Circle
- In a circle, the torque is maximum when the magnetic field is perpendicular to the plane of the circle.
- The area vector of the circle is parallel to the magnetic field, so the angle θ is 0 degrees.
- The torque in this case is given by τ = 0, as sinθ = 0.
- Therefore, the torque on a circle is zero.

Conclusion
The torque acting on the loop is maximum when the loop is in the shape of a circle. In this case, the torque is zero, indicating that no rotational force is exerted on the loop. This result can be explained by the fact that the forces on opposite sides of the loop cancel each other out, resulting in a net torque of zero.

Answer

Torque= B I N A sinø
where, B= Magnetic field
I = current in loop
N = No of turns
A= Area of loop
As we know that among any 2-D structure the area of circle is highest. From the above equation we can draw the relation that TORQUE IS DIRECTLY PROPORTIONAL TO AREA. so we get max torque for circle.

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