A current (i) carrying circular wire of radius R is placed...

A current $(i)$ carrying circular wire of radius $R$ is placed in a magnetic field $B$ perpendicular to its plane. The tension $T$ along the circumference of wire is
(a) $B \bar{R}$
(b) $2 \pi \mathrm{BiR}$
(c) $\pi B i R$
(d) $2 B i R$

Key Concepts

Current Loop in a Magnetic Field

A current loop in a magnetic field is a classic system in electromagnetism that demonstrates how distributed forces can lead to net effects such as torque and tension. Analyzing a circular loop, for instance, allows one to understand how the symmetry of the system influences the balance of forces, leading to internal stresses like tension along the loop's circumference.

Magnetic Pressure and Tension

Magnetic pressure refers to the effective mechanical stress or force per unit area exerted by a magnetic field, while magnetic tension is the resulting force along the wire that counters the magnetic pressure. In a circular current loop, these concepts are critical for understanding how the magnetic forces are distributed along the wire and how they contribute to the overall mechanical equilibrium of the loop.

Lorentz Force

This is the fundamental force experienced by a moving charge in the presence of electromagnetic fields. In the context of current-carrying conductors, the Lorentz force explains how segments of a conductor experience a force when placed in a magnetic field, which is pivotal for analyzing mechanical effects on current loops.

Force on a Current-Carrying Conductor

This concept involves determining the net force acting on a conductor carrying an electric current in a magnetic field by integrating the magnetic force along its length. It uses the idea that a current element placed in a magnetic field experiences a force proportional to the product of the current, the length of the element, and the magnetic field, relevant for evaluating the forces on different shapes of conductors.

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