Name: Study of a Voltmeter and Its Sensitivity
Uploaded: 2019-07-19
Duration: 7 min 51 s
Description: Most of us know that a voltmeter is used to measure the potential difference across 2 points in an electrical circuit. Will it affect the true values? Watch...

Question

What is a solenoid? Derive the expression for magnetic field due to a long current carrying solenoid by using Ampere's circuital law.

Accepted Answer

The term solenoid refers to a long, thin loop of wire, often wrapped around a metallic core, which produces a magnetic field when an electric current is passed through it. Solenoids are important because they can create controlled magnetic fields and can be used as electromagnets.

Ampere's circuital law states that line integral of magnetic field around any

Closed loop is equal to $μ_{\circ}$ Times the electric current flowing through the cross-section area enclosed by that loop.
Mathematically, $\oint B . dl = μI$

Let the current flowing in the solenoid having number of turns per unit length n be I.
Magnitude of magnetic field inside the solenoid is B while at outside is zero.

$Now \oint_{loop} B . dl = \int B_{ab} . L + \int B_{bc} . L' + \int B_{cd} . L + \int B_{de} . L'$

The value of first term $\int B_{ab} . L = BL$

The second and fourth term are zero because angle between magnetic field and the length loop is $90 °$ .

The third term is also zero as the value of magnetic field outside the solenoid is zero.

Total current flowing through the loop $I_{total} = (nL) I$

From Ampere's circuital law, we get $BL = μ_{\circ} (nLI)$

$\Rightarrow B = μ_{\circ} nI$

What is a solenoid? Derive the expression for magnetic field due to a long current carrying solenoid by using Ampere's circuital law.

Important Questions on Moving Charges and Magnetism

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