Physics - Magnetism Question with Solution | TestHub

PhysicsMagnetismBiot-savart's & Ampere's Circuital lawEasy2 minPYQ_2020

PhysicsEasysingle choice

One of the two identical conducting wires of length $L$ is bent in the form of a circular loop and the other one into a circular coil of $N$ identical turns. If the same current is passed in both, the ratio of the magnetic field at the centre of the loop $(B_{L})$ to that at the centre of the coil $(B_{C}),$ i.e. $\frac{B_{L}}{B_{C}}$ will be

Options:

Answer:

Solution:

For a single loop, radius

$r_{1} = \frac{L}{2 π}$

$B_{L} = \frac{μ_{0} I}{2 r_{1}} = \frac{μ_{0} I}{2 \cdot L} \times 2 π$ ...(1)

For a circular coil, radius

$r_{2} = \frac{L}{2 π N}$

$B_{c} = \frac{μ_{0} \cdot I \cdot N}{2 r_{2}} = \frac{μ_{0} \cdot I \cdot N}{2 \cdot L} \cdot 2 π N$ ...(2)

$\frac{B_{L}}{B_{C}} = \frac{1}{N^{2}}$ (from eqns (1) and (2))

Subject:PhysicsTopic:MagnetismSubtopic:Biot-savart's & Ampere's Circuital law

⏱ 2mℹ️ Source: PYQ_2020

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