Current Loop's Torque and Force [Part II]

F1 and F3

Forces that are having the same line of action and are equal and opposite, making the sum of their torques about any axis to be 0

F2 and F4

Forces that furnish any torque on the loop

x

Distance between point O and side 2

(a - x)

Distance between point O and side 4

Moment arm

The perpendicular distance from the axis of rotation to the line of action of force.

x*sin(θ) î

Moment arm of F2

(a - x)sin(θ) î

Moment arm of F4

Στ = F2*x*sin(θ) î - F4(a - x)sin(θ) î

Equation for the net torque on the loop

Στ = -IbB*xsin(θ) î - IbB*(a - x)sin(θ) î

Equation for the net torque on the loop (Substituting the definitions of F2 and F4)

τ = - I*A*B*sin(θ) î

The final form of the equation of the net torque on the loop

A = a*b

Formula for the area of the loop

x, point O

Here, the torque is independent of ; it is therefore independent of where ______ is located in the plane of the current loop.

Yes, it is true

Is it true that the loop experiences the same torque from the magnetic field about any axis in the plane of loop and parallel to the x-axis?

Magnetic dipole

A closed-current loop

μ

Symbol that represents the magnetic dipole moment

vector

Magnetic dipole moment is a ______

μ = I*A n̂

Mathematical representation of the magnetic dipole moment.

n̂

Symbol that represents a unit vector perpendicular to the plane of the loop

RHR-2

Rule to use to obtain the direction of the n̂; our thumb represents the n̂

μ = N*I*A n̂

Formula to find the magnetic dipole moment of the loop having N number of turns

τ = μ × B

The torque on a current loop due to a uniform magnetic field in term of the magnetic dipole moment (for a current loop in a 2-d plane of a shape)

U = -μ•B

Formula for the potential energy of a magnetic dipole

magnetic moment, magnetic field

The concept of aligning ______________ with the ____________ is the functionality of the devices like magnetic motors

external magnetic field, minimize, potential energy

Switching the _______________________ results in a constant spinning of the loop as it align with it, to ________ its ________________.