A loop carrying current I lies in the x y-plane in the...

A loop carrying current $I$ lies in the $x y$-plane in the figure. The unit vector $\hat{\mathbf{k}}$ is coming out of the plane of the paper. The magnetic moment of the current loop is (a) $a^{2} l \hat{k}$ (b) $\left(\frac{\pi}{2}+1\right) a^{2} l \hat{\hat{k}}$ (c) $-\left(\frac{\pi}{2}+1\right) a^{2} / \hat{k}$ (d) $(2 \pi+1) a^{2} / \hat{k}$

A loop carrying current $I$ lies in the $x y$-plane in the figure. The unit vector $\hat{\mathbf{k}}$ is coming out of the plane of the paper. The magnetic moment of the current loop is
(a) $a^{2} l \hat{k}$
(b) $\left(\frac{\pi}{2}+1\right) a^{2} l \hat{\hat{k}}$
(c) $-\left(\frac{\pi}{2}+1\right) a^{2} / \hat{k}$
(d) $(2 \pi+1) a^{2} / \hat{k}$

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Magnetic Moment

The magnetic moment is a measure of the strength and orientation of a current loop’s magnetic dipole. It is defined as the product of the current and the area vector of the loop. This concept is crucial because it determines how the current loop interacts with external magnetic fields, such as in producing a torque.

Area Vector

The area vector of a current loop is a vector perpendicular to the plane of the loop with a magnitude equal to the area enclosed by the loop. Its direction is determined by the right-hand rule, which is essential for establishing the correct orientation of physical quantities, like the magnetic moment.

Right-Hand Rule

The right-hand rule is a technique used to determine the direction of the area vector (and consequently the magnetic moment) in a current loop. By aligning the fingers with the current direction, the thumb points in the direction of the area vector. This concept plays a pivotal role in predicting the behavior of the system in a magnetic field.

Loop Geometry

The geometry of the current loop, including its size and shape, directly influences the magnitude of the magnetic moment. The loop’s physical dimensions determine the area, and thereby impact the strength of the magnetic dipole moment, an important factor in electromagnetic interactions.

Transcript

Please give Ace some feedback