Magnetic Field from Moving Charge

Questions and Answers

Match the following symbols with their meanings:

B = Magnetic field μo = Permeability of free space H = Henry V = Voltage

Match the following variables with their descriptions:

q = Charge θ = Angle k = Proportionality constant B = Magnetic field strength

Match the following constants with their values:

μo = 4π x 10^-7 H/m π = Approximately 3.14 k = 4π θ = Angle in radians

Match the following terms with their categories:

Permeability = Magnetic property H = Unit of inductance V = Electrical quantity B = Magnetic field Signup and view all the answers

Match the following equations with their components:

B = k qVsinθ = Formula for magnetic field B = μo qVsinθ/4π = Magnetic field with permeability H = μo = Definition of permeability q = Charge = Electric charge Signup and view all the answers

Match the following components with their meanings:

q = Electric charge V = Voltage applied θ = Angle in the equation μo = Permeability of vacuum Signup and view all the answers

Match the following terms with their definitions:

Vacuum = Space without matter Permeability = Ability to support magnetic field Magnetic field = Region around a magnet Inductance = Measure of opposition to change in current Signup and view all the answers

Match the following units with their associated physical quantities:

H = Inductance V = Voltage T = Tesla (Magnetic Flux Density) A = Current Signup and view all the answers

Study Notes

Magnetic Field Due to a Moving Point Charge

A point charge +Q moves in a straight line with velocity $\vec{v}$.
At a distance $r$ from the charge Q, a point P experiences a magnetic field.
The magnetic field (B) at point P is influenced by several factors related to the charge and its velocity.

Key Proportional Relationships

The magnetic field is directly proportional to the magnitude of the charge, expressed as:
- ( B \propto q )
The magnetic field is directly proportional to the velocity of the charge:
- ( B \propto V )
The sine of the angle ($\theta$) between the velocity vector ($V \vec{T}$) and the magnetic field vector ($B \vec{T}$) affects the magnetic field:
- ( B \propto \sin \theta )
The magnetic field is inversely proportional to the square of the distance (r) from the charge to the point P:
- ( B \propto \frac{1}{r^2} )

Combined Equation

The overall equation combining these relationships is:
- ( B = k q V \sin \theta )
The proportionality constant (k) is given by:
- ( k = \frac{\mu_0}{4\pi} )
The complete expression for the magnetic field in SI units is:
- ( B = \frac{\mu_0 q V \sin \theta}{4\pi} )

Constants

( \mu_0 ) represents the permeability of free space (vacuum).
The specific value of ( \mu_0 ) is:
- ( \mu_0 = 4\pi \times 10^{-7} \text{ H/m} )
Permeability of free space is also referred to as permeability of vacuum.

Description

Explore the concept of the magnetic field generated by a moving point charge. This quiz will challenge your understanding of the relationships between charge, velocity, and magnetic fields. Ideal for students studying electromagnetism and related topics.