An electron is moving in the +y -direction at 2.0 ×10^5 m / s through a uniform magnetic field

step 1 belongs to the magnetic forces in which we have an electron which is moving in the y direction w

An electron is moving in the +y -direction at 2.0 ×10^5 m /...

An electron is moving in the $+y$ -direction at $2.0 \times 10^{5} \mathrm{~m} / \mathrm{s}$ through a uniform magnetic field of $3.40 \mathrm{~T}$ in the $-x$ -direction. (a) What are the magnitude and direction of the force on the electron? (b) Find the electric field that would give zero net force on the electron.

Key Concepts

Magnetic Force on a Moving Charge

The magnetic force on a moving charge is specifically determined by the cross product F = q(v × B). Its magnitude depends on the charge, the particle’s speed, the magnetic field strength, and the sine of the angle between the velocity and magnetic field directions. The direction of this force is found using the right-hand rule, which must be adjusted when the charge is negative, meaning the force direction is opposite to that predicted for a positive charge.

Balancing Forces with an Electric Field

When the net force on a charge is desired to be zero, an external electric field can be used to counteract the magnetic force. This is achieved by setting the electric force equal in magnitude and opposite in direction to the magnetic force, leading to the condition E = - (v × B). This concept is crucial in applications where the motion of charged particles needs to be controlled or stabilized, such as in certain devices and experimental setups.

Lorentz Force Law

The Lorentz force law is fundamental in electromagnetism and describes the force experienced by a charged particle moving in electric and magnetic fields. It is given by F = q(E + v × B), where q is the charge, v is the velocity, E is the electric field, and B is the magnetic field. This law combines the effects of both electric and magnetic fields in influencing the motion of the charge.

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