Magnetism – Study Notes (TS EAMCET Physics)
Target audience: 3rd‑year engineering students preparing for the TS EAMCET exam.
Time to cover: 2 – 3 hours.
Goal: Understand concepts, remember key equations, and be able to solve typical entrance‑exam problems.
1. Simple Explanation
Magnetism is a physical phenomenon produced by moving electric charges. A magnetic field exerts a force on other moving charges or on magnetic dipoles. The magnetism we experience (magnets, compasses, electromagnets) is a macroscopic manifestation of microscopic currents (electron motion in atoms).
Key idea: A moving charge in a magnetic field experiences a force perpendicular to both its velocity and the field – the Lorentz force. This principle underpins electric motors, generators, and many practical devices.
2. Key Points & Essentials
| Topic | Core Concept | Important Formula | Notes |
|---|---|---|---|
| Magnetic Field (B) | Field produced by a current or a moving charge | - Biot–Savart Law (for a filamentary current) (\displaystyle \mathbf{B} = \frac{\mu_0 I}{4\pi}\int \frac{d\mathbf{l}\times \hat{r}}{r^2}) |
(\mu_0=4\pi\times10^{-7},{\rm H/m}) |
| - Ampère’s Law (for symmetric situations) (\displaystyle \oint \mathbf{B}\cdot d\mathbf{l}= \mu_0 I_{\rm enc}) |
Use for long straight wire, solenoid, toroid | ||
| Magnetic Force on a Charge | Lorentz force | (\displaystyle \mathbf{F}=q(\mathbf{v}\times\mathbf{B})) | Direction given by right‑hand rule (RHR) |
| Magnetic Force on a Current‑Carrying Wire | (d\mathbf{F}= I, d\mathbf{l}\times\mathbf{B}) | (\displaystyle F = I L B \sin\theta) | (\theta) = angle between (I) and (\mathbf{B}) |
| Magnetic Flux (Φ) | Total magnetic field through an area | (\displaystyle \Phi = \int \mathbf{B}\cdot d\mathbf{A} = B A \cos\theta) | Units: Weber (Wb) |
| Magnetic Circuit | Equivalent of electrical circuits for magnetic fields | (\displaystyle \mathcal{F} = \Phi R_m) (Gauss’ Law for magnetics) | (\mathcal{F}) = magnetomotive force, (R_m) = magnetic reluctance |
| Magnetic Permeability | (\displaystyle \mu = \mu_0 \mu_r) | (\mu_r = 1 + \chi_m) | (\chi_m) = magnetic susceptibility |
| Magnetic Materials | Diamagnetism, Paramagnetism, Ferromagnetism | - Diamagnetic: (\chi_m < 0) - Paramagnetic: (0<\chi_m<10^{-2}) - Ferromagnetic: (\chi_m\gg1) |
Ferromagnets have hysteresis |
| Faraday’s Law of Induction | Change in magnetic flux induces EMF | (\displaystyle \mathcal{E}= -\frac{d\Phi}{dt}) | Negative sign = Lenz’s law |
| Lenz’s Law | Induced EMF opposes change in flux | (\displaystyle \text{Direction of induced current opposite to change in }\Phi) | Key for generators |
| Motors vs Generators | Motors: electric → mechanical; Generators: mechanical → electric | Same Lorentz force principle | Use (\mathbf{F}=I L B) for torque |
| Units | (B): Tesla (T) = ( \rm{N,s,C^{-1},m^{-1}}) (\Phi): Weber (Wb) = ( \rm{T,m^2}) (\mathcal{E}): Volt (V) |
(\mu_0=4\pi\times10^{-7}) H/m |
3. Worked Example
Problem
A straight conductor of length (L = 0.5;{\rm m}) carrying a current (I = 4;{\rm A}) lies in a uniform magnetic field of magnitude (B = 0.3;{\rm T}). The conductor is oriented at an angle (\theta = 60^\circ) to the magnetic field. Find:
- The magnitude and direction of the magnetic force on the conductor.
- If the conductor rotates at a speed (\omega = 1200;{\rm rpm}) about an axis perpendicular to the field, what is the induced EMF across its ends?
Solution
1. Magnetic Force
Formula:
[
F = I L B \sin\theta
]
Plug in values:
[
F =