In this study note, we will delve into the fascinating topic of Moving Charges and Magnetism, which is a crucial part of the CBSE Physics syllabus. This topic explores how electric charges in motion create magnetic fields and how these magnetic fields interact with other charges and currents. We will break down complex ideas into manageable sections and provide examples, equations, and diagrams to make the concepts clear and easy to understand.
Hans Christian Oersted's experiment demonstrated that an electric current creates a magnetic field around it. This was a pivotal discovery that established the relationship between electricity and magnetism.
Example
If a current of 2 A flows through a straight conductor, a magnetic compass needle placed nearby will show deflection, indicating the presence of a magnetic field.
The direction of the magnetic field around a current-carrying conductor can be determined using the right-hand thumb rule.
Tip
Remember: Thumb = Current direction, Fingers = Magnetic field direction.
The magnetic field ($B$) around a straight current-carrying conductor at a distance $r$ from the conductor is given by:
$$ B = \frac{\mu_0 I}{2 \pi r} $$
where:
For a circular loop of radius $R$ carrying current $I$, the magnetic field at the center of the loop is given by:
$$ B = \frac{\mu_0 I}{2R} $$
Note
The magnetic field at the center of a circular loop is directed along the axis of the loop.
When a charged particle with charge $q$ moves with velocity $\mathbf{v}$ in a magnetic field $\mathbf{B}$, it experiences a force $\mathbf{F}$ given by the Lorentz force law:
$$ \mathbf{F} = q (\mathbf{v} \times \mathbf{B}) $$
Common Mistake
A common mistake is to use the right hand instead of the left hand for Fleming's left-hand rule. Always use the left hand to determine the direction of force.
When a charged particle moves perpendicular to a uniform magnetic field, it undergoes circular motion. The radius $r$ of the circular path is given by:
$$ r = \frac{mv}{qB} $$
where:
Example
An electron (charge $e = 1.6 \times 10^{-19} , C$) moving with a velocity of $10^6 , m/s$ perpendicular to a magnetic field of $0.01 , T$ will have a circular path radius given by:
$$ r = \frac{(9.1 \times 10^{-31} , kg) \times (10^6 , m/s)}{(1.6 \times 10^{-19} , C) \times (0.01 , T)} \approx 5.7 \times 10^{-3} , m $$
A current-carrying conductor placed in a magnetic field experiences a force given by:
$$ \mathbf{F} = I (\mathbf{L} \times \mathbf{B}) $$
where:
Two parallel conductors carrying currents $I_1$ and $I_2$ separated by a distance $d$ exert a force on each other. The force per unit length is given by:
$$ \frac{F}{L} = \frac{\mu_0 I_1 I_2}{2 \pi d} $$
Note
The force is attractive if the currents are in the same direction and repulsive if they are in opposite directions.
Faraday's law states that the induced EMF ($\varepsilon$) in a circuit is directly proportional to the rate of change of magnetic flux through the circuit:
$$ \varepsilon = -\frac{d\Phi_B}{dt} $$
where $\Phi_B$ is the magnetic flux.
Lenz's law states that the direction of the induced EMF and hence the induced current is such that it opposes the change in magnetic flux that produced it.
Common Mistake
A common mistake is to forget the negative sign in Faraday's law, which indicates the direction of the induced EMF as per Lenz's law.
Understanding the relationship between moving charges and magnetism is fundamental in physics. From the magnetic effects of electric current to the forces experienced by moving charges in magnetic fields, these principles form the basis for many technological applications, including electric motors, generators, and transformers.
By breaking down these concepts into smaller sections, providing examples, and using rules and laws, we hope this study note has made the topic more digestible and easier to understand.
Tip
Regular practice of problems and revisiting these concepts will help solidify your understanding and prepare you for exams.