A coil of $$100$$ turns and area $$2$$×$$10-2$$ $$m2$$ is pivoted about a vertical diameter in a uniform magnetic field and carries a current of $$5A$$. When the coil is held with its plane in $$north-south$$ direction, it experiences a couple of $$0.3Nm$$. When the plane is $$east-west$$, the corresponding couple is $$0.4Nm$$, the value of magnetic induction is (neglect$$ earth’s magnetic $$field)…………T.

Question

A coil of $$100$$ turns and area $$2$$×$$10-2$$ $$m2$$ is pivoted about a vertical diameter in a uniform magnetic field and carries a current of $$5A$$. When the coil is held with its plane in $$north-south$$ direction, it experiences a couple of $$0.3Nm$$. When the plane is $$east-west$$, the corresponding couple is $$0.4Nm$$, the value of magnetic induction is (neglect$$ earth’s magnetic $$field)…………T.

Infinity Learn · Accepted Answer

Torque, τ$$=BANisin$$θ⇒τ ∝Sinθ$$Case(i)$$     τ$$1$$∝Sinθ                    $$N-S$$ Case (ii)   τ$$2$$∝$$Sin(90o-$$θ$$)$$       $$E-WDividing$$ , τ$$1$$τ$$2=$$$$tan$$θ$$=0.30.4=34$$⇒Sinθ$$=35$$&Cosθ$$=45Now$$ , τ$$=BANiSin$$θ     (Consider$$ case $$(i))⇒$$B=$$τANiSinθ$$=0.32$$×$$10-2$$×$$100$$×$$5$$×$$35=0.05T$$

Applications involving charged particles moving in a magnetic field

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

Applications involving charged particles moving in a magnetic field

Remember concepts with our Masterclasses.

Torque, τ=BANisinθ⇒τ ∝SinθCase(i) τ1∝Sinθ N-S Case (ii) τ2∝Sin(90o-θ) E-WDividing , τ1τ2=tanθ=0.30.4=34⇒Sinθ=35&Cosθ=45Now , τ=BANiSinθ (Consider case (i))⇒B=τANiSinθ=0.32×10-2×100×5×35=0.05T

Ready to Test Your Skills?

free study material