A tightly wound solenoid of radius ‘ a ’ and length ‘ l ’ has n turns per unit length. It carries an electric current i . Magnetic field at a distance l 4 from one of the end (inside the solenoid on its axis) is B = μ 0 n i 5 + 3 K for l = 4 a . Then find the value of K .

Hint: B = μ 0 n i 2 s i n θ 1 + s i n θ 2 ⇒ B = μ 0 n i 2 1 2 + 3 10 ⇒ B = μ 0 n i 5 + 3 40 ∴ K = 40

Physics - Magnetism Question with Solution | TestHub

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

PhysicsEasynumerical

A tightly wound solenoid of radius $‘ a ’$ and length $‘ l ’$ hasnturns per unit length. It carries an electric currenti. Magnetic field at a distance $\frac{l}{4}$ from one of the end (inside the solenoid on its axis) is $B = \frac{μ_{0} n i (\sqrt{5} + 3)}{\sqrt{K}}$ for $l = 4 a$ . Then find the value ofK.

Answer:

40.00

Solution:

Hint: $B = \frac{μ_{0} n i}{2} [s i n θ_{1} + s i n θ_{2}]$

$\Rightarrow B = \frac{μ_{0} n i}{2} [\frac{1}{\sqrt{2}} + \frac{3}{\sqrt{10}}]$
$\Rightarrow B = \frac{μ_{0} n i (\sqrt{5} + 3)}{\sqrt{40}}$
$∴ K = 40$

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

⏱ 2mℹ️ Source: PYQ_2020

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