What is a Magnetic Field Due to Current?

When an electric current flows through a conductor, it produces a magnetic field around it. The shape and strength of the magnetic field depend on the geometry of the conductor (straight wire, coil, or solenoid) and the magnitude of the current.

Magnetic Field Due to a Straight Conductor

For a straight current-carrying conductor, the magnetic field lines form concentric circles around the conductor. The direction of the magnetic field is given by the Right-Hand Thumb Rule.

Magnetic Field Around a Straight Conductor

The magnitude of the magnetic field (B) at a distance r from a straight conductor carrying current I is given by:

Where:

• B = Magnetic field strength (in Tesla).
• μ₀ = Permeability of free space (4π × 10^-7 Tm/A).
• I = Current in the conductor (in Amperes).
• r = Distance from the conductor (in meters).

Magnetic Field Due to a Circular Loop (Coil)

For a circular loop carrying current, the magnetic field lines are circular around each segment of the loop. The field is strongest at the center of the loop.

Magnetic Field of a Circular Loop

The magnitude of the magnetic field (B) at the center of a circular loop of radius R carrying current I is given by:

Where:

• B = Magnetic field strength (in Tesla).
• μ₀ = Permeability of free space (4π × 10^-7 Tm/A).
• I = Current in the loop (in Amperes).
• R = Radius of the loop (in meters).

Magnetic Field Due to a Solenoid

A solenoid is a coil of wire wound in the shape of a helix. When current passes through it, the magnetic field inside the solenoid is uniform and resembles that of a bar magnet.

Magnetic Field of a Solenoid

The magnitude of the magnetic field (B) inside a solenoid with n turns per unit length carrying current I is given by:

Where:

• B = Magnetic field strength (in Tesla).
• μ₀ = Permeability of free space (4π × 10^-7 Tm/A).
• n = Number of turns per unit length (in turns/meter).
• I = Current in the solenoid (in Amperes).