A particle of charge q moves in a circle of radius r with...

A particle of charge $q$ moves in a circle of radius $r$ with spced $v$ Treating the circular path as a current loop with an average current,
find the maximum torque exerted on the loop by a uniform field of
magnitude $B$ .

Key Concepts

Magnetic Moment of a Current Loop

A magnetic moment is a vector quantity associated with a current loop and represents the strength and orientation of its magnetic properties. For a loop, it is calculated as the product of the current and the area of the loop. When a charged particle moves in a circular path, it can be treated as a current loop by considering the charge passing through a point per unit time, which results in an effective current.

Torque on a Magnetic Dipole

When a magnetic dipole, such as a current loop with a magnetic moment, is placed in a uniform magnetic field, it experiences a torque. This torque tends to align the magnetic moment with the external field and is given by the cross product of the magnetic moment and the magnetic field. The maximum torque occurs when the magnetic moment is perpendicular to the magnetic field, simplifying the expression to the product of the magnitudes of the magnetic moment and the magnetic field.

Effective Current from Circular Motion

A moving charge in a circular path generates an effective current by repeatedly passing through a given point in a closed loop. The effective current is determined by dividing the charge by the period of motion, which is related to the speed and circumference of the circle. This concept allows the analysis of the moving charge using the laws applicable to current loops in electromagnetism.

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