This chapter discusses the relationship between moving charges and magnetic fields. It is crucial for understanding how electric currents generate magnetic fields and the effects of these fields on charged particles.
MOVING CHARGES AND MAGNETISM – Formula & Equation Sheet
Essential formulas and equations from Physics Part - I, tailored for Class 12 in Physics.
This one-pager compiles key formulas and equations from the MOVING CHARGES AND MAGNETISM chapter of Physics Part - I. Ideal for exam prep, quick reference, and solving time-bound numerical problems accurately.
Key concepts & formulas
Essential formulas, key terms, and important concepts for quick reference and revision.
Formulas
F = q(v × B)
F is the magnetic force (in newtons), q is the charge (in coulombs), v is the velocity of the charge (in m/s), and B is the magnetic field (in teslas). This formula defines the force experienced by a charge moving in a magnetic field, crucial for understanding the motion of charged particles.
B = μ₀I / (2πr)
B is the magnetic field at a distance r from a long straight conductor carrying a current I. μ₀ is the permeability of free space (≈ 4π × 10⁻⁷ T m/A). This relationship explores how magnetic fields emanate from current-carrying wires.
F = IlB sin(θ)
F is the force on a current-carrying conductor, I is the current (in amperes), l is the length of the wire (in meters), B is the magnetic field (in teslas), and θ is the angle between l and B. This formula is useful for finding the force on a wire in a magnetic field.
r = mv / (qB)
r is the radius of the circular path, m is mass (in kg), v is velocity (in m/s), q is charge (in coulombs), and B is the magnetic field (in teslas). It defines the radius of a charged particle's circular motion in a magnetic field.
ω = qB / m
ω is the angular frequency, q is charge (in coulombs), B is magnetic field (in teslas), and m is mass (in kg). It shows the rate of rotation of a charged particle in a magnetic field.
B = μ₀nI
B is the magnetic field inside a long solenoid, I is the current (in amperes), n is the number of turns per unit length (in turns/m). This formula is pivotal for magnetic fields generated by solenoids.
τ = m × B
τ is the torque on the magnetic moment m (in Am²) placed in a magnetic field B (in teslas). Torque indicates the potential for rotational motion of a current loop in a magnetic field.
E = (1/2)mv²
E is kinetic energy (in joules), m is mass (in kg), and v is velocity (in m/s). This general expression helps calculate the energy of a charged particle moving in fields.
F = BIL
F is the force (in newtons) on a length L of wire carrying current I in a magnetic field B (in teslas). This is a simplified version of calculating forces in magnetic fields relevant for specific exams.
Equations
Lorentz Force: F = q(E + v × B)
Describes the force acting on a charged particle in both electric (E) and magnetic (B) fields.
Biot-Savart Law: dB = (μ₀/4π) (Idl × r̂) / r²
Calculates the magnetic field dB due to an infinitesimal segment of current Idl at distance r.
Ampere's Law: ∫B·dl = μ₀I
Relates the integrated magnetic field around a closed loop to the total current I passing through the enclosed area.
B = μ₀I / (2R) for circular loop
Defines the magnetic field at the center of a circular loop of radius R carrying a current I.
F = μ₀I₁I₂ / (2πd)
Force per unit length between two parallel conductors carrying currents I₁ and I₂, separated by distance d.
m = NIA
Magnetic moment m represents the strength of a magnetic dipole, where N is number of turns, I is current and A is area.
F_ba = μ₀I_aI_bL / (2πd)
This equation defines the force between two parallel currents in terms of their separation distance d.
p = I_A sin(θ)
Calculates the magnetic torque acting on a current loop, where θ is the angle between field lines and the moment.
E = qV
Energy gained by charge q when moved through a potential difference V.
B = (μ₀ / 4π) * (2I / d)
Magnetic field produced by a straight current-carrying wire at a distance r from the wire.
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