When a current carrying circular loop is placed in a magnetic field it...
Explanation of the Formula for Torque on a Current-Carrying Circular Loop in a Magnetic Field
The Formula
The formula for the torque on a current-carrying circular loop in a magnetic field is given by:
τ = IABsinθ
where τ is the torque, I is the current, A is the area of the loop, B is the magnetic field strength, and θ is the angle between the magnetic field and the plane of the loop.
The Two Forces
When a current-carrying circular loop is placed in a magnetic field, two equal and opposite forces act on it. The magnitude of each force is given by:
F = IBL
where F is the force, I is the current, B is the magnetic field strength, and L is the length of the loop.
The Net Force
Since the two forces are equal and opposite, they cancel out each other and the net force on the loop is zero.
The Magnitude of Torque
The magnitude of the torque on the loop is given by:
τ = F x 2r
where r is the radius of the loop.
The 4 Factor
The original formula does not include the factor of 4. However, it is important to note that the formula assumes that the loop is a rectangle with sides of length L and 2r. In reality, the loop is a circle with a diameter of 2r. Therefore, the actual area of the loop is πr^2, which is four times smaller than the area assumed in the formula.
So, the correct formula for the torque on a current-carrying circular loop in a magnetic field is:
τ = 4IArB
where A is the area of the loop, which is equal to πr^2.