Magnetic Fields due to Electric Current
Easy Overview
Ever noticed how a compass needle moves when you bring it near a wire carrying current? That's because moving charges create magnetic fields. This chapter is all about the connection between electricity and magnetism — every current makes a magnetic field, and magnetic fields push on currents.
Biot-Savart Law
The Biot-Savart law tells you the magnetic field produced by a tiny piece of current-carrying wire. The field gets weaker as you move farther away (1/r²), and it's strongest in the direction perpendicular to the wire. It's like the smoke from a cigarette — the smoke intensity decreases as you move away, and it's strongest straight above the tip. This law is the starting point for calculating magnetic fields for any current-carrying shape — straight wires, loops, solenoids, you name it.
Ampere's Law
Ampere's law is the magnetic equivalent of Gauss's law. It says the total magnetic field around any closed loop is proportional to the current passing through the loop. If you wrap an imaginary loop around a current-carrying wire, the magnetic field along that loop times the loop length equals μ₀ times the current inside. It's the easiest way to find the magnetic field for symmetrical situations — straight wires, solenoids, toroids. No messy integration required.
Force on a Current in a Magnetic Field
A current-carrying wire in a magnetic field feels a force. That's the motor effect. The force depends on the current, the length of wire in the field, the strength of the magnetic field, and the angle between the wire and the field. Maximum force when the wire is perpendicular to the field, zero when it's parallel. This is how electric motors work — loops of wire in a magnetic field experience forces that make them spin. It's also how speakers work — current in a coil creates a force that moves the speaker cone.
Solenoids and Toroids
A solenoid is just a coil of wire. When current flows through it, it produces a nearly uniform magnetic field inside, like a bar magnet. One end acts as north pole, the other as south. The field inside depends only on the number of turns per unit length and the current — not on the diameter. A toroid is a solenoid bent into a donut shape. Its magnetic field is confined entirely within the donut. Solenoids are used in electromagnets, doorbells, and relays — anywhere you need to convert electrical current into mechanical motion.
Key Points
- •Biot-Savart law gives magnetic field due to a current element: dB = (μ₀/4π)(Idℓ×r̂/r²).
- •Ampere's law: ∮B·dℓ = μ₀I_enclosed.
- •Force on a current-carrying conductor: F = BIL sinθ. Direction given by Fleming's left-hand rule.
- •Magnetic field inside a solenoid B = μ₀nI, where n = N/L.
- •A current loop acts as a magnetic dipole with magnetic moment m = NIA.
- •Moving coil galvanometer uses the torque on a current loop in a magnetic field to measure current.
Practice Questions
- State Ampere's law. Use it to find the magnetic field inside a solenoid and a toroid.
- Derive the expression for the force between two parallel current-carrying conductors.
- Explain the working of a moving coil galvanometer. How is it converted into an ammeter and voltmeter?
- A circular coil of radius 10 cm has 100 turns and carries a current of 5 A. Find the magnetic field at its centre.