A uniform magnetic field of 0.50 T is directed to the north. At some instant, a particle with c

step 1 Okay, so we have a charged particle moving enough magnetic field. The magnetic field is directed

A uniform magnetic field of 0.50 T is directed to the...

A uniform magnetic field of $0.50 \mathrm{~T}$ is directed to the north. At some instant, a particle with charge $+0.020 \mu \mathrm{C}$ is moving with velocity $2.0 \mathrm{~m} / \mathrm{s}$ in a direction $30^{\circ}$ north of east. (a) What is the magnitude of the magnetic force on the charged particle? (b) What is the direction of the magnetic force?

Key Concepts

Magnetic Force on a Moving Charge

This concept describes the force experienced by a charged particle when it moves through a magnetic field. The force is calculated using the equation F = q(v × B), where q is the charge, v is the velocity, and B is the magnetic field. The magnitude of the force depends on the charge, the speed of the particle, the strength of the magnetic field, and the sine of the angle between the velocity and the magnetic field vectors.

Vector Cross Product

The vector cross product is a mathematical operation used to compute the magnetic force on a moving charge. It produces a vector that is perpendicular to the plane formed by the velocity and magnetic field vectors, which is essential for determining both the magnitude (F = qvB sin?) and the direction of the magnetic force.

Right-Hand Rule

The right-hand rule is a mnemonic used to determine the direction of the magnetic force resulting from the cross product of the velocity and magnetic field vectors. By orienting the fingers of the right hand in the direction of the velocity and curling them toward the magnetic field, the thumb then points in the direction of the force for a positive charge.

Uniform Magnetic Field

A uniform magnetic field is one in which the magnetic induction is constant in magnitude and direction throughout a given region. This uniformity simplifies the analysis of the motion of charged particles and the computation of the magnetic force they experience, as the field does not vary with position.

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