(II) An electron experiences the greatest force as it travels 2.8 ×10^6 m/s in a magnetic field

step 1 Question number 18 asks us to work backwards a little bit. We're told that we have an electron t

(II) An electron experiences the greatest force as it...

(II) An electron experiences the greatest force as it travels 2.8 $\times$ 10$^6$ m/s in a magnetic field when it is moving northward. The force is vertically upward and of magnitude 6.2 $\times$ 10$^{-13}$ N. What is the magnitude and direction of the magnetic field?

Key Concepts

Lorentz Force

The Lorentz force is the combined electric and magnetic force on a point charge due to electromagnetic fields. In the absence of an electric field, a moving charge in a magnetic field experiences a force perpendicular to both its velocity and the magnetic field, governed by the equation F = q(v × B). This principle is fundamental to understanding how charged particles interact with magnetic fields.

Magnetic Force Equation

The magnetic force experienced by a moving charge is quantified by the equation F = qvB sin(?), where q is the charge, v is the speed of the particle, B is the magnetic field strength, and ? is the angle between the velocity vector and the magnetic field. Maximum force is achieved when the velocity is perpendicular to the magnetic field (? = 90°), making the sine term equal to 1.

Cross Product and Vector Direction

The force on a charged particle moving in a magnetic field is determined by the cross product of the velocity and magnetic field vectors. This cross product results in a vector (the force) that is perpendicular to the plane formed by the velocity and magnetic field vectors, and its direction is given by the rules of vector cross product.

Charge Sign and Force Direction

The sign of the charge influences the direction of the magnetic force. For positively charged particles, the direction of the force is given by the right-hand rule, whereas for electrons (which carry a negative charge), the force direction is opposite to that predicted by the right-hand rule. This concept is crucial in determining the actual direction of the force experienced by electrons in magnetic fields.

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