A particle with a charge of +10.0 μC is moving at 300 ·m / s in the positive z -direction. a) Fi

step 1 question, we have a particle with charge Q equals to plus 10 .0 microculum and it is moving with

A particle with a charge of +10.0 μC is moving at 300 ·m / s...

A particle with a charge of $+10.0 \mu \mathrm{C}$ is moving at $300 \cdot \mathrm{m} / \mathrm{s}$ in the positive $z$ -direction. a) Find the minimum magnetic field required to keep it moving in a straight line at constant speed if there is a uniform electric field of magnitude $100 . \mathrm{V} / \mathrm{m}$ pointing in the positive $y$ -direction. b) Find the minimum magnetic field required to keep the particle moving in a straight line at constant speed if there is a uniform electric field of magnitude $100 . \mathrm{V} / \mathrm{m}$ pointing in the positive $z$ -direction.

A particle with a charge of $+10.0 \mu \mathrm{C}$ is moving at $300 \cdot \mathrm{m} / \mathrm{s}$ in the positive $z$ -direction.
a) Find the minimum magnetic field required to keep it moving in a straight line at constant speed if there is a uniform electric field of magnitude $100 . \mathrm{V} / \mathrm{m}$ pointing in the positive $y$ -direction.
b) Find the minimum magnetic field required to keep the particle moving in a straight line at constant speed if there is a uniform electric field of magnitude $100 . \mathrm{V} / \mathrm{m}$ pointing in the positive $z$ -direction.

Key Concepts

Lorentz Force Law

The Lorentz force law is a fundamental equation that describes the total force experienced by a charged particle moving in electric and magnetic fields. It states that the net force is the sum of the electric force (qE) and the magnetic force (qv x B). This law is essential for understanding how charged particles behave under the influence of electromagnetic fields and is the foundation for analyzing their trajectories.

Electric Force

The electric force on a charged particle is given by qE, where q is the charge and E is the electric field. This force acts in the direction of the electric field for a positive charge and opposite for a negative charge. Recognizing the role of the electric force is important in problems where an external electric field influences the motion of a particle.

Magnetic Force

The magnetic force on a charged particle moving in a magnetic field is described by q(v x B), where v is the velocity of the particle and B is the magnetic field. This force is always perpendicular to both the velocity and the magnetic field. Understanding the magnetic force is crucial in scenarios where the motion of a charged particle needs to be controlled or modified by applying magnetic fields.

Force Balance for Equilibrium

When a charged particle moves with constant speed in a straight line, the net force acting on it must be zero according to Newton’s first law. In the context of electromagnetic fields, this implies that the magnetic force can be used to cancel out the electric force. Setting qE equal to q(vB) (or relating their vector components appropriately) allows one to determine the necessary conditions for achieving force balance and maintaining constant velocity.

Right-Hand Rule

The right-hand rule is a mnemonic used to determine the direction of the magnetic force on a positive charge moving in a magnetic field. By pointing the fingers of the right hand in the direction of the velocity and curling them towards the direction of the magnetic field, the thumb points in the direction of the force. This concept is crucial for predicting and understanding the vector nature of the forces involved in electromagnetic interactions.

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