# Calculating the Force and Torque on a current loop

• Physicslearner500039
In summary, the conversation discussed the forces and torque calculations for a system with a magnetic moment and magnetic field that are 180 degrees apart. The net force was found to be 0, indicating an unstable equilibrium. The conversation also mentioned the difficulty in calculating angles and recommended a textbook for further understanding.
Physicslearner500039
Homework Statement
A rectangular coil of wire, 22.0 cm by 35.0 cm and carrying a current of 1.40 A, is oriented with the plane of its loop perpendicular to a uniform 1.50-T magnetic field, as shown in Fig.
(a) Calculate the net force and torque that the magnetic field exerts on the coil.
(b) The coil is rotated through a 30 Deg angle about the axis shown, with the left side coming out of the plane of the figure and the right side going into the plane. Calculate the net force and torque that the magnetic field now exerts on the coil.
Relevant Equations
F = IlBsin(Θ); Toque = Magnetic moment * Magnetic Field
##\vec \tau = \vec \mu \times \vec B -eq1##
## F = I \vec l \times \vec B -eq2 ##
The forces i have indicated

The magnetic moment is coming out of the page.
I am only attempting only the part (a) as of now
a. The force calculations are
F1 = 1.4*0.22*1.5 = 0.462 +X direction
F2 = 1.4*0.22*1.5 = -0.462 -X direction
F3 = 1.4*.35*1.5 = 0.735 +Y direction
F4 = 1.4*.35*1.5 = -0.735 -Y direction
The net force is 0.
b. The Torque as per eq1 cross product of magnetic moment and the magnetic field. Since they are 180 Deg apart, the Torque is 0. Since they are 180 Deg apart the system is unstable and the coil starts moving. Am I correct? Please advise.

Physicslearner500039 said:
Since they are 180 Deg apart the system is unstable
Does that suffice to show instability? What if the forces were directed outwards from the loop?

Physicslearner500039
haruspex said:
Does that suffice to show instability? What if the forces were directed outwards from the loop?
There was only a one line in the textbook that if angle between the Magnetic moment and Magnetic field is 180, it is in an unstable equilibrium. I don't know much apart from that.

Regarding the Part b problem, I am finding extremely difficult to imagine and calculate the angles. Do you recommend any mathematical textbook chapter which has such kind of problems for me to solve and gain confidence.

Physicslearner500039 said:
if angle between the Magnetic moment and Magnetic field is 180, it is in an unstable equilibrium
Ah, ok. I thought you meant that the forces on opposite sides of the loop were 180 degrees out from each other, as in your diagram.
Physicslearner500039 said:
Regarding the Part b problem
See if the second part of http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magmom.html helps.

Physicslearner500039

## What is the formula for calculating the force on a current loop?

The formula for calculating the force on a current loop is F = I * L * B * sin(theta), where I is the current, L is the length of the loop, B is the magnetic field strength, and theta is the angle between the current and the magnetic field.

## How do you calculate the torque on a current loop?

The torque on a current loop can be calculated using the formula T = I * A * B * sin(theta), where I is the current, A is the area of the loop, B is the magnetic field strength, and theta is the angle between the current and the magnetic field.

## What is the direction of the force on a current loop?

The direction of the force on a current loop is determined by the right-hand rule. If the current is flowing in the same direction as the magnetic field, the force will be in the opposite direction of the magnetic field. If the current is flowing in the opposite direction, the force will be in the same direction as the magnetic field.

## How does increasing the current affect the force and torque on a current loop?

Increasing the current in a current loop will result in a greater force and torque. This is because the force and torque are directly proportional to the current. Therefore, the greater the current, the greater the force and torque on the loop.

## What factors can affect the force and torque on a current loop?

The force and torque on a current loop can be affected by the strength and direction of the magnetic field, the current in the loop, and the size and orientation of the loop. Additionally, the presence of other nearby currents or magnetic materials can also impact the force and torque on the loop.

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