What is the primary condition for a current loop to experience torque in a magnetic field?

The primary condition is that the current loop must be placed in an external magnetic field, and its magnetic dipole moment vector must not be perfectly aligned or anti-aligned with the magnetic field vector. If the magnetic dipole moment $\vec{M}$ is parallel or anti-parallel to the magnetic field $\vec{B}$ (i.e., $\theta = 0^\circ$ or $180^\circ$), the torque will be zero. For any other orientation, a torque will act on the loop, tending to rotate it until $\vec{M}$ aligns with $\vec{B}$.

Why is the net force on a current loop in a uniform magnetic field zero, but the torque is not necessarily zero?

In a uniform magnetic field, for every segment of current-carrying wire in the loop, there is an equal and opposite segment (or combination of segments) experiencing an equal and opposite force. Therefore, the vector sum of all forces over the entire closed loop is zero. However, these equal and opposite forces might not act along the same line of action. When forces form a 'couple' (equal, opposite, and non-collinear), they produce a net turning effect, or torque, even if the net translational force is zero.

How does the angle $\theta$ in the torque formula $\tau = NIAB \sin\theta$ relate to the orientation of the loop?

The angle $\theta$ in the formula $\tau = NIAB \sin\theta$ is the angle between the magnetic dipole moment vector $\vec{M}$ of the loop and the external magnetic field vector $\vec{B}$. The magnetic dipole moment vector $\vec{M}$ is defined as a vector perpendicular to the plane of the loop, with its direction determined by the right-hand rule (curl fingers in current direction, thumb points to $\vec{M}$). Therefore, if the plane of the loop makes an angle $\alpha$ with the magnetic field, then $\theta = 90^\circ - \alpha$.

When is the torque on a current loop maximum and minimum?

The torque on a current loop is given by $\tau = NIAB \sin\theta$. It is maximum when $\sin\theta = 1$, which means $\theta = 90^\circ$. This occurs when the magnetic dipole moment vector $\vec{M}$ is perpendicular to the magnetic field $\vec{B}$, or equivalently, when the plane of the loop is parallel to the magnetic field. The torque is minimum (zero) when $\sin\theta = 0$, which means $\theta = 0^\circ$ or $\theta = 180^\circ$. This occurs when $\vec{M}$ is parallel or anti-parallel to $\vec{B}$, meaning the plane of the loop is perpendicular to the magnetic field.

What is the significance of the magnetic dipole moment $\vec{M}$ in understanding torque on a current loop?

The magnetic dipole moment $\vec{M}$ simplifies the understanding and calculation of torque. It encapsulates the properties of the loop (number of turns $N$, current $I$, and area $A$) into a single vector quantity. The torque can then be expressed elegantly as a vector cross product $\vec{\tau} = \vec{M} \times \vec{B}$. This formulation highlights that the torque's magnitude depends on the magnitudes of $\vec{M}$ and $\vec{B}$ and the sine of the angle between them, and its direction is perpendicular to both, tending to align $\vec{M}$ with $\vec{B}$.

Can a current loop experience a net force in a magnetic field?

Yes, but only if the magnetic field is non-uniform. In a uniform magnetic field, the net force on any closed current loop is always zero. However, if the magnetic field varies across the loop (i.e., it's non-uniform), the forces on different segments might not perfectly cancel out, leading to a net translational force in addition to a torque. This principle is used in some magnetic levitation systems.

Torque on Current Loop

Physics

NEET UG

Version 1Updated 22 Mar 2026

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A current-carrying loop, when placed in a uniform external magnetic field, experiences a net torque. This torque tends to align the magnetic dipole moment of the loop with the direction of the external magnetic field. While the net force on a current loop in a uniform magnetic field is zero, the forces acting on different segments of the loop are generally not collinear, leading to a rotational ef…

Quick Summary

A current-carrying loop placed in an external magnetic field experiences a torque. This torque arises because the forces acting on different segments of the loop, due to the magnetic field, are generally not collinear, even though the net force on the loop in a uniform magnetic field is zero.

The magnitude of the torque ( $\tau$ ) on a loop with $N$ turns, carrying current $I$ , enclosing area $A$ , and placed in a magnetic field $B$ , is given by $\tau = NIAB \sin\theta$ . Here, $\theta$ is the angle between the normal to the plane of the loop (which defines the magnetic dipole moment $\vec{M}$ ) and the magnetic field $\vec{B}$ .

The magnetic dipole moment is defined as $\vec{M} = NIA \hat{n}$ , where $\hat{n}$ is the unit vector normal to the loop's plane. In vector form, the torque is $\vec{\tau} = \vec{M} \times \vec{B}$ . The torque tends to align the magnetic dipole moment $\vec{M}$ with the magnetic field $\vec{B}$ .

Maximum torque occurs when the plane of the loop is parallel to the field ( $\theta = 90^\circ$ ), and zero torque occurs when the plane is perpendicular to the field ( $\theta = 0^\circ$ or $180^\circ$ ).

This phenomenon is fundamental to the operation of electric motors and galvanometers.

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Potential Energy and Equilibrium

The potential energy $U$ of a magnetic dipole in a magnetic field is given by $U = -\vec{M} \cdot \vec{B} =…

Force on current segment: —

d\vec{F} = I(d\vec{l} \times \vec{B})

Magnetic Dipole Moment: —

\vec{M} = NIA \hat{n}

(magnitude

M=NIA

)

Torque on Current Loop: —

\vec{\tau} = \vec{M} \times \vec{B}

Magnitude of Torque: —

\tau = NIAB \sin\theta

* $\theta$ : Angle between $\vec{M}$ (normal to loop) and $\vec{B}$ . * If angle between plane and $\vec{B}$ is $\alpha$ , then $\theta = 90^\circ - \alpha$ .

Maximum Torque: —

\tau_{max} = NIAB

(when

\theta = 90^\circ

, plane parallel to

\vec{B}

)

Zero Torque: —

\tau = 0

(when

\theta = 0^\circ

180^\circ

, plane perpendicular to

\vec{B}

)

Potential Energy: —

U = -\vec{M} \cdot \vec{B} = -MB \cos\theta

Stable Equilibrium: —

\theta = 0^\circ

U = -MB

(minimum potential energy,

\vec{M} \parallel \vec{B}

)

Unstable Equilibrium: —

\theta = 180^\circ

U = +MB

(maximum potential energy,

\vec{M} \uparrow\downarrow \vec{B}

)

Net Force in Uniform B: —

\vec{F}_{net} = 0

Galvanometer Principle: —

NIAB = k\phi

(for radial field,

\sin\theta = 1

)

To remember the torque formula and angle: 'M-B-Sin-Theta, Normal-to-Plane is Theta'

M-B-Sin-Theta: — Reminds you

\tau = MB \sin\theta

Normal-to-Plane is Theta: — Emphasizes that

\theta

is the angle between the magnetic moment (which is normal to the plane) and the magnetic field, not the plane itself.