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Question

Two wires A and B have the same length equal to 44 cm and carry a current of 10 A each. Wire A is bent into a circle and wire B into a square. (a) Which wire produces a greater magnetic field at the centre? (b) Obtain the magnitudes of the field at the centres of the two wires.

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Solution

Given that,

Length = 44 cm

Current = 10 A

Now, for circle

the length is bent in form of circle then the circumference is

2πr=44

r=442π

Now, the magnetic field is

BA=μ0I2πr

BA=4π×107×10×2π2×44×102

BA=0.89×104T

Now, for square

Length 44 cm is form in square

So, each side has length 11 cm

Now, the magnetic field due to first wire at the center

B=μ0I4πa(cos450+cos450)

Now, due to the all four wires

BB=4μ0I4πa(cos450+cos450)

BB=4×4π×107×10×2×24π×11×2×102

BB=1.02×104T

Hence, the square loop will have more magnetic field at the center


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