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

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

Grade:12

2 Answers

Saurabh Koranglekar
askIITians Faculty 10341 Points
one year ago
576-1620_as.PNG
Vikas TU
14149 Points
one year ago
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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