Govt. Exams
Entrance Exams
For circular motion in a magnetic field: qvB = mv²/r, which gives r = mv/(qB). Therefore, momentum p = mv = qBr = eBr (for an electron where q = e).
Magnetic moment M = IA, where I is the current and A is the area enclosed by the loop. For N turns, M = NIA. The SI unit is A·m².
The magnetic field inside an ideal long solenoid is B = μ₀nI, independent of the solenoid's radius and position along the axis (away from ends). This assumes n is the number of turns per unit length.
When a charged particle moves perpendicular to a uniform magnetic field, the Lorentz force acts as centripetal force, causing circular motion. The radius is r = mv/(qB).
Parallel wires carrying currents in the same direction experience attractive force. Force per unit length = μ₀I₁I₂/(2πd). If currents are opposite, the force is repulsive.
The magnetic force on a current-carrying conductor is F = BIL sinθ, where θ is the angle between the current direction and the magnetic field. When θ = 90°, force is maximum (BIL), and when θ = 0°, force is zero.
Magnetic field lines always form closed loops and cannot exist in isolation. Unlike electric field lines which start from positive charges and end at negative charges, magnetic field lines have no beginning or end.
By Faraday's law, induced EMF = -dΦ/dt. Magnetic flux Φ = BA = πr²B. As B changes from 0 to B₀ in time t, EMF = πr²(B₀-0)/t = πr²B₀/t
Motional EMF = BLv (where L is perpendicular to both B and v)
A shunt (low resistance in parallel) diverts excess current, protecting the galvanometer coil
