A 0.45 -T magnetic field points due east. (a) Find the...

A 0.45 -T magnetic field points due east. (a) Find the magnitude and direction of the force on a $+0.10-\mu$ C charge moving southward at $3.5 \mathrm{~m} / \mathrm{s}$. (b) Repeat for a $-0.10-\mu \mathrm{C}$ charge with the same velocity.

Key Concepts

Lorentz Force

The Lorentz force describes the force on a charged particle moving in an electromagnetic field. In the context of a magnetic field, the force is given by F = q(v × B), meaning that the magnitude and direction of the force depend on the charge, its velocity, and the magnetic field. This principle is fundamental in understanding how charged particles interact with magnetic fields, influencing the design of devices like cyclotrons, mass spectrometers, and electric motors.

Cross Product

The cross product is a mathematical operation applied to two vectors that results in a third vector perpendicular to both. When calculating the magnetic force, the cross product of the velocity vector and the magnetic field vector determines the direction of the force, with its magnitude depending on the sine of the angle between the two vectors. This operation is central to vector calculus and physics, particularly in electromagnetism.

Right-Hand Rule

The right-hand rule is a mnemonic used to determine the direction of the resultant vector in a cross product. For a positive charge, pointing the fingers of the right hand in the direction of the velocity and curling them towards the magnetic field gives the direction of the force. This rule is crucial for visualizing and properly applying the cross product in magnetic force problems.

Sign of the Charge

The sign of the charge is essential in determining the actual direction of the force exerted by the magnetic field. For a positive charge, the force direction follows the right-hand rule directly, while for a negative charge, the force direction is opposite to that predicted by the right-hand rule. This concept is key in understanding phenomena in electromagnetic interactions and the behavior of charged particles within magnetic fields.

Transcript

Please give Ace some feedback