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

step 1 So we can find the magnetic field using equation 27 .5p. Now since the magnetic field and veloci

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

(II) An electron experiences the greatest force as it travels $2.8 \times 10^{6} \mathrm{m} / \mathrm{s}$ in a magnetic field when it is moving north- ward. The force is vertically upward and of magnitude $8.2 \times 10^{-13} \mathrm{N} .$ What is the magnitude and direction of the magnetic field?

(II) An electron experiences the greatest force as it travels
$2.8 \times 10^{6} \mathrm{m} / \mathrm{s}$ in a magnetic field when it is moving north-
ward. The force is vertically upward and of magnitude
$8.2 \times 10^{-13} \mathrm{N} .$ What is the magnitude and direction of the
magnetic field?

Key Concepts

Right-Hand Rule

The right-hand rule is a mnemonic that helps determine the direction of the force resulting from the cross product of two vectors. In the context of magnetic forces, it indicates the direction of force on a positive charge moving in a magnetic field. However, when dealing with electrons (which have a negative charge), the resulting force is in the opposite direction, making this rule a critical tool for analyzing particle motion in magnetic fields.

Charge and its Effect on Force Direction

The nature of the charge (positive or negative) plays an important role in determining the direction of the magnetic force. For negatively charged particles such as electrons, the direction of the Lorentz force is reversed compared to the prediction of the right-hand rule for positive charges. This concept is key to correctly interpreting the force direction in problems involving charged particles in magnetic fields.

Lorentz Force

The Lorentz force describes the force exerted on a charged particle moving in an electromagnetic field. It is given by the equation F = q(v × B), where q is the charge, v is the velocity, and B is the magnetic field. This concept is crucial in understanding how charged particles interact with magnetic fields, which directly applies to determining the magnitude and direction of the magnetic force in the problem.

Vector Cross Product

The vector cross product is a mathematical operation used to calculate the magnitude and direction of the force on a moving charge in a magnetic field. Because the force is determined by the product of the velocity and magnetic field vectors, understanding the properties of the cross product—particularly its dependence on the sine of the angle between the vectors—is essential in solving such problems.

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