A particle with a charge of +8.4 μC and a speed of 45 m / s enters a uniform magnetic field who

step 1 Let us solve the part A of this problem. The force acting on the particle in a magnetic field ca

A particle with a charge of +8.4 μC and a speed of 45 m / s...

A particle with a charge of $+8.4 \mu \mathrm{C}$ and a speed of $45 \mathrm{~m} / \mathrm{s}$ enters a uniform magnetic field whose magnitude is $0.30 \mathrm{~T}$. For each of the cases in the drawing, find the magnitude and direction of the magnetic force on the particle.

Key Concepts

Magnetic Force

Magnetic force is the force exerted on a moving electric charge by a magnetic field. This force is always perpendicular to both the velocity of the charged particle and the magnetic field lines, causing the particle to change direction but not speed, provided no other forces act on it.

Lorentz Force Law

The Lorentz force law quantifies the total force experienced by a charged particle moving in electric and magnetic fields. In scenarios involving only a magnetic field, the force is given by F = q v B sin(?), where q is the charge, v is the speed of the particle, B is the magnitude of the magnetic field, and ? is the angle between the velocity and the magnetic field vectors.

Vector Cross Product

The calculation of the magnetic force involves the vector cross product, which means that the resultant force vector is perpendicular to the plane formed by the velocity and the magnetic field vectors. The magnitude of this force depends on the sine of the angle between the two vectors and maximizes when they are perpendicular.

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 pointing the fingers of the right hand in the direction of the velocity vector and curling them toward the magnetic field vector, the thumb points in the direction of the force acting on a positive charge.

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