This chapter explores how electric currents create magnetic effects and their applications.
Magnetic Effects of Electric Current – Formula & Equation Sheet
Essential formulas and equations from Science, tailored for Class X in Science.
This one-pager compiles key formulas and equations from the Magnetic Effects of Electric Current chapter of Science. 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 = BIL sinθ
F is the force (in newtons) on a current-carrying conductor, B is the magnetic field strength (in tesla), I is the current (in amperes), L is the length of the conductor (in meters), and θ is the angle between the conductor and the magnetic field. This formula calculates the force experienced by a conductor in a magnetic field.
B = μ₀I / (2πr)
B is the magnetic field strength (in tesla) around a straight conductor, μ₀ is the permeability of free space (4π × 10⁻⁷ Tm/A), I is the current (in amperes), and r is the distance from the conductor (in meters). This formula gives the magnetic field at a distance r from a long straight conductor.
B = μ₀nI
B is the magnetic field strength (in tesla) inside a solenoid, μ₀ is the permeability of free space, n is the number of turns per unit length, and I is the current (in amperes). This formula calculates the uniform magnetic field inside a solenoid.
Φ = BA cosθ
Φ is the magnetic flux (in weber), B is the magnetic field strength (in tesla), A is the area (in square meters), and θ is the angle between the field and the normal to the area. This formula measures the amount of magnetic field passing through a given area.
F = qvB sinθ
F is the force (in newtons) on a moving charge, q is the charge (in coulombs), v is the velocity (in meters per second), B is the magnetic field strength (in tesla), and θ is the angle between the velocity and the magnetic field. This formula calculates the Lorentz force on a moving charge.
Equations
Right-Hand Thumb Rule
If the thumb of the right hand points in the direction of the current, the curled fingers indicate the direction of the magnetic field lines around the conductor. This rule helps determine the direction of the magnetic field generated by a current.
Fleming’s Left-Hand Rule
Stretch the thumb, forefinger, and middle finger of the left hand mutually perpendicular. If the forefinger points in the direction of the magnetic field and the middle finger in the direction of the current, the thumb points in the direction of the force. This rule predicts the direction of force on a current-carrying conductor in a magnetic field.
Magnetic Field due to a Circular Loop: B = μ₀I / (2R)
B is the magnetic field (in tesla) at the center of a circular loop, μ₀ is the permeability of free space, I is the current (in amperes), and R is the radius of the loop (in meters). This equation calculates the magnetic field at the center of a current-carrying loop.
Force between Two Parallel Conductors: F/L = μ₀I₁I₂ / (2πd)
F/L is the force per unit length (in newtons per meter) between two parallel conductors, μ₀ is the permeability of free space, I₁ and I₂ are the currents (in amperes) in the conductors, and d is the distance between them (in meters). This equation determines the attractive or repulsive force between two parallel current-carrying wires.
Electromagnetic Induction: ε = -N ΔΦ/Δt
ε is the induced electromotive force (in volts), N is the number of turns in the coil, ΔΦ is the change in magnetic flux (in weber), and Δt is the time interval (in seconds). This equation, Faraday's law, quantifies the induced EMF due to changing magnetic flux.
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