Question

The magnetic field due to a current carrying circular loop of radius 3cm at o point on the axis at a distance of 4cm from the centre is 54micro Tesla.what will be its value at the centre of the loop?

Answer 1

   We are given a circular current carrying conducting loop. Need to find the magnetic field B (flux density) at a distance d from the center of the loop along the axis of the loop.   Using Biot-Savart's law for magnetic field we can derive the formula.

Current through the loop = i
B = 54 * 10⁻⁶ T
d = 4 cm = 0.04 m
radius = a = 3 cm = 0.03 m

               B = μ i a² / [2 (d² + a²)³/² ]
               54 * 10⁻⁶  = 4 π * 10⁻⁷ * i * 0.03² / [2 * 0.05³]   T
=>        i  = 1.193 Amp

Magnetic field at the center of the loop is given by

    B = μ i / (2 a)
        = 4 π * 10⁻⁷ * 1.193 /(2 * 0.03) T
        = 2.50 * 10⁻⁵ T