SATHEE: moving-charges-and-magnetism Question 46

moving-charges-and-magnetism Question 46

Question: Q. 2. (a) Write the expression for the equivalent magnetic moment of a planer current loop of area $A$ , having $N$ turns and carrying a current $i$ . Use the expression to find the magnetic dipole moment of a revolving electron.

(b) A circular loop of radius $r$ , having $N$ turns and carrying current $I$ , is kept in the $X Y$ plane. It is then subjected to a uniform magnetic field $B = B_{x} \hat{I} +$ $B_{y} \hat{J} + B_{z} \hat{k}$ . Obtain expression for the magnetic potential energy of the coil-magnetic field system.

R&A [CBSE SQP 2018-19]

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Solution:

Ans. (a) The equivalent magnetic moment is given by $μ = NiA 1 / 2$ The direction of $μ$ is perpendicular to the plane of current carrying loop. It is directed along the direction of advance of a right-handed screw rotated along the direction of flow of current. $1 / 2$ Derivation of expression for $μ$ of electron revolving around a nucleus

(b) for the loop,

$\vec{μ} = N (μ r^{2}) i (\pm \hat{k}) 1 / 2$

Magnetic potential energy $= \vec{μ} \cdot \vec{B}$

$= N (μ r^{2}) i (\pm \hat{k}) \cdot (B_{x} \hat{i} + B_{y} \hat{j} + B_{z} \hat{k})$

$= \pm r^{2} N I B_{z}$ .

$1 / 2$

[CBSE Marking Scheme, 2018-19]

Detailed Answer :

(a) The equivalent magnetic moment is given by $μ = N i A$ The direction of $μ$ is perpendicular to the plane of current carrying loop. It in directed along the direction of advance of a right handed screw rotated along the direction of flow of current. $1 / 2$ Derivation :

Let us consider an atom with an electron revolving around the nucleus.

Charge on electron is $e$ . Let its mass be $m$ .

Radius of electron’s orbit is $r$ .

Area of electron’s orbit is $A = π r^{2}$

Magnetic dipole moment of the atom is,

$μ = i A N$

The current $i$ is given by,

$i = \frac{e}{T}$

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Moving Charges And Magnetism

moving-charges-and-magnetism Question 46

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Moving Charges And Magnetism

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