At a given instant, a particle with a mass of 5.00 ×10^-3 kg and a charge of 3.50 ×10^-8 C has a

step 1 Here we have a following situation. A particle of a given mass is moving in a positive y directi

At a given instant, a particle with a mass of 5.00 ×10^-3 kg...

At a given instant, a particle with a mass of $5.00 \times 10^{-3} \mathrm{kg}$ and a charge of $3.50 \times 10^{-8} \mathrm{C}$ has a velocity with a magnitude of $2.00 \times 10^{5} \mathrm{m} / \mathrm{s}$ in the $+y$ direction. It is moving in a uniform magnetic field that has magnitude 0.8 $\mathrm{T}$ and is in the $-x$ direction. What are (a) the magnitude and direction of the magnetic force on the particle and (b) its resulting acceleration?

Key Concepts

Lorentz Force

The Lorentz force is the combined force experienced by a charged particle moving in electric and magnetic fields. In problems where only a magnetic field is present, the force is given by the equation F = q(v × B), where q is the charge, v is the velocity, and B is the magnetic field.

Magnetic Force on Moving Charges

When a charged particle moves through a magnetic field, it experiences a force that is perpendicular to both its velocity and the magnetic field. This force is calculated by the magnitude q·v·B·sin(?), with ? representing the angle between the velocity and magnetic field vectors.

Vector Cross Product

The vector cross product is a mathematical operation used to determine a vector that is perpendicular to two given vectors. It is essential in determining both the magnitude and the direction of the magnetic force, as the force direction follows from the cross product (v × B).

Right-Hand Rule

The right-hand rule is a standard technique used to find the direction of the cross product of two vectors. In the context of magnetic forces, aligning the fingers in the direction of the velocity and curling them toward the magnetic field allows one to determine that the thumb points in the direction of the force on a positive charge.

Newton's Second Law

Newton's Second Law links the net force acting on an object to its mass and the resulting acceleration, as expressed by F = ma. This principle is used to convert the magnetic force acting on a charged particle into its corresponding acceleration.

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