A wire of length 0.26 m is bent to form a circular loop if 2 A of current is flowing through the loop calculate magnetic field at a point P which is at a distance 0.15 m from its centre
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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
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