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A uniform magnetic field of 3000 G is established along the positive z-direction. A rectangular loop of sides 10 cm and 5 cm carries a current of 12 A. What is the torque on the loop in the different cases shown in Fig.? What is the force in each case? Which case corresponds to stable equilibrium?
420513_52a5df20b5c84e83bd1759dccdbd9766.png

Solution
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(a)
A=l×b=50×104
τ=IA×B=1.8×102^jNm
Force is zero because θ=0
τ is along negative y-direction.


(b)A=l×b=50×104

τ=IA×B=1.8×102^jNm

Force is zero because θ=0

τ is along negative y-direction.


(c)A=l×b=50×104

τ=IA×B=1.8×102^iNm

Force is zero because θ=0

τ is along negative x-direction.


(d)A=l×b=50×104

|τ|=IAB=1.8×102Nm at angle of 240o with x-direction.

Force is zero because θ=0


(e)A=l×b=50×104

τ=IA×B

A is parallel to B. So, τ=0

So, Force is zero.Since the angle is 0o, if disturbed it doesn't come back to the original position.


(f)A=l×b=50×104

τ=IA×B

A is opposite to B, i.e., θ=180o.

So, τ=0

So, Force is zero.Since the angle is 180o, if disturbed it doesn't come back to the original position.

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