A 0.950 -T magnetic field points due north. (a) Find the...

A 0.950 -T magnetic field points due north. (a) Find the magnitude and direction of the force on a $+1.40-\mu \mathrm{C}$ charge moving westward at $1.50 \mathrm{~m} / \mathrm{s}$ (b) Repeat for a $-1.40-\mu \mathrm{C}$ charge with the same velocity.

Key Concepts

Right-Hand Rule

The right-hand rule is a mnemonic used to determine the direction of the force on a positive charge moving in a magnetic field. For a positive charge, if you point your fingers in the direction of the current (velocity) and curl them toward the magnetic field, your thumb points in the direction of the force.

Lorentz Force

The Lorentz force is the fundamental concept describing the force experienced by a charged particle moving in a magnetic 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.

Magnetic Field

A magnetic field is a vector field that exerts a force on moving electric charges. Its existence and orientation define the environment in which charged particles experience forces, influencing their trajectory according to both magnitude and direction.

Vector Cross Product

The vector cross product is a mathematical operation used to calculate the magnitude and direction of the force resulting from the interaction between two vectors. In the context of magnetic forces, it is used to compute the cross product of the velocity vector and the magnetic field vector.

Impact of Charge Sign

The sign of the charge is critical in determining the direction of the force. For positive charges, the force follows the direction given by the right-hand rule, whereas for negative charges, the force is in the opposite direction, effectively reversing the outcome of the right-hand rule.

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