Question

a circular loop of radius R is kept in a uniform magnetic field pointing perpendicular into the plane of paper. when a current I flows in the loop, the tension produced in the loop is​

Answer 1

Let a small elementary length dl cut into circle as shown in figure, dθ is the angle subtended by dl into centre of circle . so, elementary length , dl = Rdθ

Now, F = I(dl × B)

= Idl.Bsin90° [ because elementary length are perpendicular upon magnetic field ]

= BIRdθ

Also tension acts on just opposite side of force as you can see in figure .

So, at equilibrium condition ,

2Tsindθ/2 = BIRdθ

actually, dθ/2 is very small angle so, sindθ/2 ≈ dθ/2

Hence, 2Tdθ/2 = BIRdθ

T = BIR

hence tension in the loop is BIR