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Standard XII

Physics

More about Magnetic Dipoles

A circular lo...

Question

A circular loop carrying a current i is made of a wire of length L. A uniform magnetic field B exists parallel to the plane of the loop. (a) Find the torque on the loop. (b) If the same length of the wire is used to form a square loop, what would be the torque? Which is larger?

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Solution

Given,
Magnetic field intensity = B
Circumference, L = 2πr, where r is the radius of the coil.
So, area of the coil, A $= \frac{L^{2}}{4 π}$
Magnitude of current = i
Torque acting on the coil,
τ = niABsinθ, where θ is the angle between the area vector and the magnetic field.
$τ = n i A B = \frac{i L^{2} B}{4 π}$
(b) Let s be the length of the square loop.
$4 s = L \Rightarrow s = \frac{L}{4} A = {(\frac{L}{4})}^{2} = (\frac{L^{2}}{16}) τ = n i A B = \frac{i L^{2} B}{16}$
So, the torque on the circular loop is larger.

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