# The case that has the highest torque on the loop

• Fatima Hasan
In summary, In the attempt to solve the homework statement, the student used the equations T = IAB sin θ and T = μ × B. T = 0 was found because θ = 0. T = 0 was found because θ = 180°. T = (k)×(k) was found because the fingers points to the direction of current and the thump points to the direction of T. T = (-k) × (-k) was found because the direction of μ = -k. The area is 2a*b and the angle is 90°.
Fatima Hasan

## Homework Equations

T = IAB sin θ ; θ is the angle between B and I.
T = μ × B

## The Attempt at a Solution

A) T = IAB sin θ
T = √2 a b I B (θ = 45°)
B) T = 0 , because θ = 0
C) T = 0 , because θ =180°
D) T = μ × B
The direction of μ = -k , because the fingers points to the direction of current and the thump points to the direction of T.
T = (-k) × (-k)
=0
E) T = (k)×(k)
=0
So , the answer is 'A' .
Is it correct ?

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Unfortunately, no. :)

In your analysis of A, B, and C, you're only accounting for one side of each rectangle--the one labeled with an "I" in the diagram. In fact, in the formula ##| \mathbf{\tau} | = IAB \sin(\theta)##, the angle ##\theta## is meant to be taken between the current loop's normal vector and the magnetic field, *not* between the current and ##\mathbf{B}##. This is actually a consequence of the second formula you gave, ##\mathbf{\tau} = \mathbf{\mu} \times \mathbf{B}##, since the magnetic moment of a current loop is ##IA \mathbf{n}## (where ##\mathbf{n}## is the positively-oriented unit norm to the loop).

So actually, ##\theta = 90^{\circ}## in each of choices A, B, and C. Given this, what should the answer be?

Last edited:
VKint said:
So actually, ##\theta = 90^{\circ}## in each of choices A, B, and C.
And in 'D' and 'E' , ##\theta = 0^{\circ}## ?

VKint said:
In your analysis of A, B, and C, you're only accounting for one side of each rectangle--the one labeled with an "I" in the diagram.
Should I multiply by 4 ?

In D and E, ##\theta## is either ##0## or ##180^{\circ}##; in either case the torque vanishes.

Multiplying by 4 won't solve the problem. The issue is that the magnetic field makes a different angle with each of the sides of the loop. The correct way to account for this is by using the magnetic moment of the loop *as a whole* instead of trying to add up the torques on each side.

VKint said:
The correct way to account for this is by using the magnetic moment of the loop *as a whole*
T = μ × B
= I A B sin θ
The area is 2a*b and the angle is 90°.
So, T = 2 I a b B
Right ?

## 1. What is torque and how does it relate to the loop?

Torque is the measure of the rotational force applied to an object. In the case of a loop, torque is the force that causes the loop to rotate around its axis. The higher the torque, the more likely the loop is to rotate.

## 2. How is the torque on the loop calculated?

The torque on a loop can be calculated by multiplying the force applied to the loop by the distance between the force and the axis of rotation. The direction of the force also plays a role in determining the torque.

## 3. What factors contribute to the highest torque on the loop?

The factors that contribute to the highest torque on a loop include the magnitude of the force applied, the distance between the force and the axis of rotation, and the direction of the force. A larger force, a greater distance, and a perpendicular force will all result in a higher torque.

## 4. How does the shape of the loop affect the torque?

The shape of the loop can affect the torque by changing the distance between the force and the axis of rotation. A loop with a larger radius will have a greater distance and therefore a higher torque compared to a loop with a smaller radius.

## 5. How can the torque on the loop be increased or decreased?

The torque on the loop can be increased by increasing the force applied, increasing the distance between the force and the axis of rotation, or changing the direction of the force to be more perpendicular to the loop. It can be decreased by doing the opposite, such as reducing the force or decreasing the distance between the force and the axis of rotation.

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