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PHXII04:MOVING CHARGES AND MAGNETISM

363019 Assertion :
When radius of circular loop carrying current is doubled, its magnetic moment becomes four times.
Reason :
Magnetic moment does not depend on area of the loop.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.

3 Assertion is correct but Reason is incorrect.

4 Assertion is incorrect but reason is correct.

Explanation:

$M = n i A, A = π r^{2}$ Doubling the radius $(r)$ , magnetic moment $M$ of a current loop increases its magnetic moment fourfold, as the magnetic dipole moment is directly proportional to the product of the current $(i)$ and the loop's area $(A)$ . So correct option is (3).

PHXII04:MOVING CHARGES AND MAGNETISM

363020 A square loop of side $l$ carries a current $i$ . It is placed as shown in figure. The magnetic moment of the loop is
supporting img

1

i l^{2} \hat{i}

2

\frac{i l^{2}}{\sqrt{2}} (\hat{i} + \hat{j})

3

i l^{2} \hat{k}

4

i l^{2} (- \hat{k})

Explanation:

Magnetic moment of current loop is $= i \vec{A}$

PHXII04:MOVING CHARGES AND MAGNETISM

363021 In the figure shown, a coil of single turn is wound on a sphere of radius $r$ and mass $m$ . The plane of the coil is parallel to the inclined plane and lies in the equatorial plane of the sphere. If the sphere is in rotational equlibrium, the value of $B$ is (current in the coil is $i$ )
supporting img

1

\frac{mg}{π ir}

2

\frac{mgr \sin θ}{π i}

3

\frac{m g \sin θ}{π i}

4 None of these

Explanation:

The gravitational torque must be counter balanced by the magnetic about $O$ , for equilibrium of the sphere.
The gravitational torque $= τ_{g r} = m g \times r \sin θ$
$\Rightarrow τ_{g r} = m g r \sin θ$
The magnetic torque, $τ_{m} = M \times B$
Magnetic torque on the coil does not depends on point of measurement.
where the magnetic moment of the coil $M = (i π r^{2})$
supporting img
$\Rightarrow τ_{m} = π i r^{2} B \sin θ$
$\Rightarrow π i r^{2} B \sin θ = m g r \sin θ$
or $B = m g / π i r$

PHXII04:MOVING CHARGES AND MAGNETISM

363022 A wire of length ' $L$ ' is shaped into a circle and then bent in such a way that the two semicircles are perpendicular. The magnetic moment of the system when current I flows through the system is

1

\frac{\sqrt{2} L^{2} I}{8 π}

2

\frac{\sqrt{3} L^{2} I}{4 π}

3

\frac{L^{2} I}{4 π}

4

\frac{L^{2} I}{2 π}

Explanation:

$μ = \frac{I L^{2}}{4 π}, μ^{1} = \sqrt{2} \frac{M}{2} \Rightarrow μ^{1} = \frac{\sqrt{2} I L^{2}}{8 π}$

PHXII04:MOVING CHARGES AND MAGNETISM

363023 A current $I$ flows in a rectangulary shaped wire whose center lies at $(x_{0}, 0, 0)$ and whose vertices are located at the points $A (x_{0} + d, - a, - b)$ , $B (x_{0} - d, a, - b),$ $C (x_{0} - d, a, b),$ and $D (x_{0} + d, - a, b)$ respectively. Assume that $a, b, d << x_{0}$ . What is the magnitude of magnetic dipole vector of the rectangular wire frame? (Given : $b = 10 m,$ $d = 12 m,$ $a = 5 m,$ $I = 0.03 A)$

1

15.6 J T^{- 1}

2

12.5 J T^{- 1}

3

10.2 J T^{- 1}

4

20.1 J T^{- 1}

Explanation:

Magnetic moment of a current carrying loop,
$\vec{m} = I \vec{S}$ [where $\vec{S}$ : area vector]
Area of loop,
$\vec{S} = \vec{A B} \times \vec{B C}$
Here, $\vec{A B} = (- 2 d \hat{i}) + 2 a \hat{j}, \vec{B C} = 2 b \hat{k}$
$∴ \vec{S} = [\begin{matrix} (B_{x} - A_{x}) \hat{i} + (B_{y} - A_{y}) \hat{j} + \\ (B_{z} - A_{z}) \hat{k} \end{matrix}]$
$\times [(C_{x} - B_{x}) \hat{i} + (C_{y} - B_{y}) \hat{j} + (C_{z} - B_{z}) \hat{k}]$
$= [x_{0} - d - x_{0} - d] \hat{i} + (a + a) \hat{j} + (- b + b) \hat{k}]$
$\times [(x_{0} - d - x_{0} + d) \hat{i} + (a - a) \hat{j} + (b + b) \hat{k}]$
$∴ \vec{s} = (- 2 d \hat{i} + 2 a \hat{j}) \times (2 b \hat{k}) = 4 b d \hat{j} + 4 a b \hat{i}$
$| \vec{m} | = I | \vec{S} |$
$= 4 I b \sqrt{a^{2} + d^{2}}$
$= 4 \times (0.03) (10) \sqrt{12^{2} + 5^{2}}$
$= 4 \times 0.3 \times 13 = 15.6 J T^{- 1}$

PHXII04:MOVING CHARGES AND MAGNETISM

363019 Assertion :
When radius of circular loop carrying current is doubled, its magnetic moment becomes four times.
Reason :
Magnetic moment does not depend on area of the loop.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.

3 Assertion is correct but Reason is incorrect.

4 Assertion is incorrect but reason is correct.

Explanation:

$M = n i A, A = π r^{2}$ Doubling the radius $(r)$ , magnetic moment $M$ of a current loop increases its magnetic moment fourfold, as the magnetic dipole moment is directly proportional to the product of the current $(i)$ and the loop's area $(A)$ . So correct option is (3).

PHXII04:MOVING CHARGES AND MAGNETISM

363020 A square loop of side $l$ carries a current $i$ . It is placed as shown in figure. The magnetic moment of the loop is
supporting img

1

i l^{2} \hat{i}

2

\frac{i l^{2}}{\sqrt{2}} (\hat{i} + \hat{j})

3

i l^{2} \hat{k}

4

i l^{2} (- \hat{k})

Explanation:

Magnetic moment of current loop is $= i \vec{A}$

PHXII04:MOVING CHARGES AND MAGNETISM

363021 In the figure shown, a coil of single turn is wound on a sphere of radius $r$ and mass $m$ . The plane of the coil is parallel to the inclined plane and lies in the equatorial plane of the sphere. If the sphere is in rotational equlibrium, the value of $B$ is (current in the coil is $i$ )
supporting img

1

\frac{mg}{π ir}

2

\frac{mgr \sin θ}{π i}

3

\frac{m g \sin θ}{π i}

4 None of these

Explanation:

The gravitational torque must be counter balanced by the magnetic about $O$ , for equilibrium of the sphere.
The gravitational torque $= τ_{g r} = m g \times r \sin θ$
$\Rightarrow τ_{g r} = m g r \sin θ$
The magnetic torque, $τ_{m} = M \times B$
Magnetic torque on the coil does not depends on point of measurement.
where the magnetic moment of the coil $M = (i π r^{2})$
supporting img
$\Rightarrow τ_{m} = π i r^{2} B \sin θ$
$\Rightarrow π i r^{2} B \sin θ = m g r \sin θ$
or $B = m g / π i r$

PHXII04:MOVING CHARGES AND MAGNETISM

363022 A wire of length ' $L$ ' is shaped into a circle and then bent in such a way that the two semicircles are perpendicular. The magnetic moment of the system when current I flows through the system is

1

\frac{\sqrt{2} L^{2} I}{8 π}

2

\frac{\sqrt{3} L^{2} I}{4 π}

3

\frac{L^{2} I}{4 π}

4

\frac{L^{2} I}{2 π}

Explanation:

$μ = \frac{I L^{2}}{4 π}, μ^{1} = \sqrt{2} \frac{M}{2} \Rightarrow μ^{1} = \frac{\sqrt{2} I L^{2}}{8 π}$

PHXII04:MOVING CHARGES AND MAGNETISM

363023 A current $I$ flows in a rectangulary shaped wire whose center lies at $(x_{0}, 0, 0)$ and whose vertices are located at the points $A (x_{0} + d, - a, - b)$ , $B (x_{0} - d, a, - b),$ $C (x_{0} - d, a, b),$ and $D (x_{0} + d, - a, b)$ respectively. Assume that $a, b, d << x_{0}$ . What is the magnitude of magnetic dipole vector of the rectangular wire frame? (Given : $b = 10 m,$ $d = 12 m,$ $a = 5 m,$ $I = 0.03 A)$

1

15.6 J T^{- 1}

2

12.5 J T^{- 1}

3

10.2 J T^{- 1}

4

20.1 J T^{- 1}

Explanation:

Magnetic moment of a current carrying loop,
$\vec{m} = I \vec{S}$ [where $\vec{S}$ : area vector]
Area of loop,
$\vec{S} = \vec{A B} \times \vec{B C}$
Here, $\vec{A B} = (- 2 d \hat{i}) + 2 a \hat{j}, \vec{B C} = 2 b \hat{k}$
$∴ \vec{S} = [\begin{matrix} (B_{x} - A_{x}) \hat{i} + (B_{y} - A_{y}) \hat{j} + \\ (B_{z} - A_{z}) \hat{k} \end{matrix}]$
$\times [(C_{x} - B_{x}) \hat{i} + (C_{y} - B_{y}) \hat{j} + (C_{z} - B_{z}) \hat{k}]$
$= [x_{0} - d - x_{0} - d] \hat{i} + (a + a) \hat{j} + (- b + b) \hat{k}]$
$\times [(x_{0} - d - x_{0} + d) \hat{i} + (a - a) \hat{j} + (b + b) \hat{k}]$
$∴ \vec{s} = (- 2 d \hat{i} + 2 a \hat{j}) \times (2 b \hat{k}) = 4 b d \hat{j} + 4 a b \hat{i}$
$| \vec{m} | = I | \vec{S} |$
$= 4 I b \sqrt{a^{2} + d^{2}}$
$= 4 \times (0.03) (10) \sqrt{12^{2} + 5^{2}}$
$= 4 \times 0.3 \times 13 = 15.6 J T^{- 1}$

PHXII04:MOVING CHARGES AND MAGNETISM

363019 Assertion :
When radius of circular loop carrying current is doubled, its magnetic moment becomes four times.
Reason :
Magnetic moment does not depend on area of the loop.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.

3 Assertion is correct but Reason is incorrect.

4 Assertion is incorrect but reason is correct.

Explanation:

$M = n i A, A = π r^{2}$ Doubling the radius $(r)$ , magnetic moment $M$ of a current loop increases its magnetic moment fourfold, as the magnetic dipole moment is directly proportional to the product of the current $(i)$ and the loop's area $(A)$ . So correct option is (3).

PHXII04:MOVING CHARGES AND MAGNETISM

363020 A square loop of side $l$ carries a current $i$ . It is placed as shown in figure. The magnetic moment of the loop is
supporting img

1

i l^{2} \hat{i}

2

\frac{i l^{2}}{\sqrt{2}} (\hat{i} + \hat{j})

3

i l^{2} \hat{k}

4

i l^{2} (- \hat{k})

Explanation:

Magnetic moment of current loop is $= i \vec{A}$

PHXII04:MOVING CHARGES AND MAGNETISM

363021 In the figure shown, a coil of single turn is wound on a sphere of radius $r$ and mass $m$ . The plane of the coil is parallel to the inclined plane and lies in the equatorial plane of the sphere. If the sphere is in rotational equlibrium, the value of $B$ is (current in the coil is $i$ )
supporting img

1

\frac{mg}{π ir}

2

\frac{mgr \sin θ}{π i}

3

\frac{m g \sin θ}{π i}

4 None of these

Explanation:

The gravitational torque must be counter balanced by the magnetic about $O$ , for equilibrium of the sphere.
The gravitational torque $= τ_{g r} = m g \times r \sin θ$
$\Rightarrow τ_{g r} = m g r \sin θ$
The magnetic torque, $τ_{m} = M \times B$
Magnetic torque on the coil does not depends on point of measurement.
where the magnetic moment of the coil $M = (i π r^{2})$
supporting img
$\Rightarrow τ_{m} = π i r^{2} B \sin θ$
$\Rightarrow π i r^{2} B \sin θ = m g r \sin θ$
or $B = m g / π i r$

PHXII04:MOVING CHARGES AND MAGNETISM

363022 A wire of length ' $L$ ' is shaped into a circle and then bent in such a way that the two semicircles are perpendicular. The magnetic moment of the system when current I flows through the system is

1

\frac{\sqrt{2} L^{2} I}{8 π}

2

\frac{\sqrt{3} L^{2} I}{4 π}

3

\frac{L^{2} I}{4 π}

4

\frac{L^{2} I}{2 π}

Explanation:

$μ = \frac{I L^{2}}{4 π}, μ^{1} = \sqrt{2} \frac{M}{2} \Rightarrow μ^{1} = \frac{\sqrt{2} I L^{2}}{8 π}$

PHXII04:MOVING CHARGES AND MAGNETISM

363023 A current $I$ flows in a rectangulary shaped wire whose center lies at $(x_{0}, 0, 0)$ and whose vertices are located at the points $A (x_{0} + d, - a, - b)$ , $B (x_{0} - d, a, - b),$ $C (x_{0} - d, a, b),$ and $D (x_{0} + d, - a, b)$ respectively. Assume that $a, b, d << x_{0}$ . What is the magnitude of magnetic dipole vector of the rectangular wire frame? (Given : $b = 10 m,$ $d = 12 m,$ $a = 5 m,$ $I = 0.03 A)$

1

15.6 J T^{- 1}

2

12.5 J T^{- 1}

3

10.2 J T^{- 1}

4

20.1 J T^{- 1}

Explanation:

Magnetic moment of a current carrying loop,
$\vec{m} = I \vec{S}$ [where $\vec{S}$ : area vector]
Area of loop,
$\vec{S} = \vec{A B} \times \vec{B C}$
Here, $\vec{A B} = (- 2 d \hat{i}) + 2 a \hat{j}, \vec{B C} = 2 b \hat{k}$
$∴ \vec{S} = [\begin{matrix} (B_{x} - A_{x}) \hat{i} + (B_{y} - A_{y}) \hat{j} + \\ (B_{z} - A_{z}) \hat{k} \end{matrix}]$
$\times [(C_{x} - B_{x}) \hat{i} + (C_{y} - B_{y}) \hat{j} + (C_{z} - B_{z}) \hat{k}]$
$= [x_{0} - d - x_{0} - d] \hat{i} + (a + a) \hat{j} + (- b + b) \hat{k}]$
$\times [(x_{0} - d - x_{0} + d) \hat{i} + (a - a) \hat{j} + (b + b) \hat{k}]$
$∴ \vec{s} = (- 2 d \hat{i} + 2 a \hat{j}) \times (2 b \hat{k}) = 4 b d \hat{j} + 4 a b \hat{i}$
$| \vec{m} | = I | \vec{S} |$
$= 4 I b \sqrt{a^{2} + d^{2}}$
$= 4 \times (0.03) (10) \sqrt{12^{2} + 5^{2}}$
$= 4 \times 0.3 \times 13 = 15.6 J T^{- 1}$

PHXII04:MOVING CHARGES AND MAGNETISM

363019 Assertion :
When radius of circular loop carrying current is doubled, its magnetic moment becomes four times.
Reason :
Magnetic moment does not depend on area of the loop.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.

3 Assertion is correct but Reason is incorrect.

4 Assertion is incorrect but reason is correct.

Explanation:

$M = n i A, A = π r^{2}$ Doubling the radius $(r)$ , magnetic moment $M$ of a current loop increases its magnetic moment fourfold, as the magnetic dipole moment is directly proportional to the product of the current $(i)$ and the loop's area $(A)$ . So correct option is (3).

PHXII04:MOVING CHARGES AND MAGNETISM

363020 A square loop of side $l$ carries a current $i$ . It is placed as shown in figure. The magnetic moment of the loop is
supporting img

1

i l^{2} \hat{i}

2

\frac{i l^{2}}{\sqrt{2}} (\hat{i} + \hat{j})

3

i l^{2} \hat{k}

4

i l^{2} (- \hat{k})

Explanation:

Magnetic moment of current loop is $= i \vec{A}$

PHXII04:MOVING CHARGES AND MAGNETISM

363021 In the figure shown, a coil of single turn is wound on a sphere of radius $r$ and mass $m$ . The plane of the coil is parallel to the inclined plane and lies in the equatorial plane of the sphere. If the sphere is in rotational equlibrium, the value of $B$ is (current in the coil is $i$ )
supporting img

1

\frac{mg}{π ir}

2

\frac{mgr \sin θ}{π i}

3

\frac{m g \sin θ}{π i}

4 None of these

Explanation:

The gravitational torque must be counter balanced by the magnetic about $O$ , for equilibrium of the sphere.
The gravitational torque $= τ_{g r} = m g \times r \sin θ$
$\Rightarrow τ_{g r} = m g r \sin θ$
The magnetic torque, $τ_{m} = M \times B$
Magnetic torque on the coil does not depends on point of measurement.
where the magnetic moment of the coil $M = (i π r^{2})$
supporting img
$\Rightarrow τ_{m} = π i r^{2} B \sin θ$
$\Rightarrow π i r^{2} B \sin θ = m g r \sin θ$
or $B = m g / π i r$

PHXII04:MOVING CHARGES AND MAGNETISM

363022 A wire of length ' $L$ ' is shaped into a circle and then bent in such a way that the two semicircles are perpendicular. The magnetic moment of the system when current I flows through the system is

1

\frac{\sqrt{2} L^{2} I}{8 π}

2

\frac{\sqrt{3} L^{2} I}{4 π}

3

\frac{L^{2} I}{4 π}

4

\frac{L^{2} I}{2 π}

Explanation:

$μ = \frac{I L^{2}}{4 π}, μ^{1} = \sqrt{2} \frac{M}{2} \Rightarrow μ^{1} = \frac{\sqrt{2} I L^{2}}{8 π}$

PHXII04:MOVING CHARGES AND MAGNETISM

363023 A current $I$ flows in a rectangulary shaped wire whose center lies at $(x_{0}, 0, 0)$ and whose vertices are located at the points $A (x_{0} + d, - a, - b)$ , $B (x_{0} - d, a, - b),$ $C (x_{0} - d, a, b),$ and $D (x_{0} + d, - a, b)$ respectively. Assume that $a, b, d << x_{0}$ . What is the magnitude of magnetic dipole vector of the rectangular wire frame? (Given : $b = 10 m,$ $d = 12 m,$ $a = 5 m,$ $I = 0.03 A)$

1

15.6 J T^{- 1}

2

12.5 J T^{- 1}

3

10.2 J T^{- 1}

4

20.1 J T^{- 1}

Explanation:

Magnetic moment of a current carrying loop,
$\vec{m} = I \vec{S}$ [where $\vec{S}$ : area vector]
Area of loop,
$\vec{S} = \vec{A B} \times \vec{B C}$
Here, $\vec{A B} = (- 2 d \hat{i}) + 2 a \hat{j}, \vec{B C} = 2 b \hat{k}$
$∴ \vec{S} = [\begin{matrix} (B_{x} - A_{x}) \hat{i} + (B_{y} - A_{y}) \hat{j} + \\ (B_{z} - A_{z}) \hat{k} \end{matrix}]$
$\times [(C_{x} - B_{x}) \hat{i} + (C_{y} - B_{y}) \hat{j} + (C_{z} - B_{z}) \hat{k}]$
$= [x_{0} - d - x_{0} - d] \hat{i} + (a + a) \hat{j} + (- b + b) \hat{k}]$
$\times [(x_{0} - d - x_{0} + d) \hat{i} + (a - a) \hat{j} + (b + b) \hat{k}]$
$∴ \vec{s} = (- 2 d \hat{i} + 2 a \hat{j}) \times (2 b \hat{k}) = 4 b d \hat{j} + 4 a b \hat{i}$
$| \vec{m} | = I | \vec{S} |$
$= 4 I b \sqrt{a^{2} + d^{2}}$
$= 4 \times (0.03) (10) \sqrt{12^{2} + 5^{2}}$
$= 4 \times 0.3 \times 13 = 15.6 J T^{- 1}$

PHXII04:MOVING CHARGES AND MAGNETISM

363019 Assertion :
When radius of circular loop carrying current is doubled, its magnetic moment becomes four times.
Reason :
Magnetic moment does not depend on area of the loop.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.

2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.

3 Assertion is correct but Reason is incorrect.

4 Assertion is incorrect but reason is correct.

Explanation:

$M = n i A, A = π r^{2}$ Doubling the radius $(r)$ , magnetic moment $M$ of a current loop increases its magnetic moment fourfold, as the magnetic dipole moment is directly proportional to the product of the current $(i)$ and the loop's area $(A)$ . So correct option is (3).

PHXII04:MOVING CHARGES AND MAGNETISM

363020 A square loop of side $l$ carries a current $i$ . It is placed as shown in figure. The magnetic moment of the loop is
supporting img

1

i l^{2} \hat{i}

2

\frac{i l^{2}}{\sqrt{2}} (\hat{i} + \hat{j})

3

i l^{2} \hat{k}

4

i l^{2} (- \hat{k})

Explanation:

Magnetic moment of current loop is $= i \vec{A}$

PHXII04:MOVING CHARGES AND MAGNETISM

363021 In the figure shown, a coil of single turn is wound on a sphere of radius $r$ and mass $m$ . The plane of the coil is parallel to the inclined plane and lies in the equatorial plane of the sphere. If the sphere is in rotational equlibrium, the value of $B$ is (current in the coil is $i$ )
supporting img

1

\frac{mg}{π ir}

2

\frac{mgr \sin θ}{π i}

3

\frac{m g \sin θ}{π i}

4 None of these

Explanation:

The gravitational torque must be counter balanced by the magnetic about $O$ , for equilibrium of the sphere.
The gravitational torque $= τ_{g r} = m g \times r \sin θ$
$\Rightarrow τ_{g r} = m g r \sin θ$
The magnetic torque, $τ_{m} = M \times B$
Magnetic torque on the coil does not depends on point of measurement.
where the magnetic moment of the coil $M = (i π r^{2})$
supporting img
$\Rightarrow τ_{m} = π i r^{2} B \sin θ$
$\Rightarrow π i r^{2} B \sin θ = m g r \sin θ$
or $B = m g / π i r$

PHXII04:MOVING CHARGES AND MAGNETISM

363022 A wire of length ' $L$ ' is shaped into a circle and then bent in such a way that the two semicircles are perpendicular. The magnetic moment of the system when current I flows through the system is

1

\frac{\sqrt{2} L^{2} I}{8 π}

2

\frac{\sqrt{3} L^{2} I}{4 π}

3

\frac{L^{2} I}{4 π}

4

\frac{L^{2} I}{2 π}

Explanation:

$μ = \frac{I L^{2}}{4 π}, μ^{1} = \sqrt{2} \frac{M}{2} \Rightarrow μ^{1} = \frac{\sqrt{2} I L^{2}}{8 π}$

PHXII04:MOVING CHARGES AND MAGNETISM

363023 A current $I$ flows in a rectangulary shaped wire whose center lies at $(x_{0}, 0, 0)$ and whose vertices are located at the points $A (x_{0} + d, - a, - b)$ , $B (x_{0} - d, a, - b),$ $C (x_{0} - d, a, b),$ and $D (x_{0} + d, - a, b)$ respectively. Assume that $a, b, d << x_{0}$ . What is the magnitude of magnetic dipole vector of the rectangular wire frame? (Given : $b = 10 m,$ $d = 12 m,$ $a = 5 m,$ $I = 0.03 A)$

1

15.6 J T^{- 1}

2

12.5 J T^{- 1}

3

10.2 J T^{- 1}

4

20.1 J T^{- 1}

Explanation:

Magnetic moment of a current carrying loop,
$\vec{m} = I \vec{S}$ [where $\vec{S}$ : area vector]
Area of loop,
$\vec{S} = \vec{A B} \times \vec{B C}$
Here, $\vec{A B} = (- 2 d \hat{i}) + 2 a \hat{j}, \vec{B C} = 2 b \hat{k}$
$∴ \vec{S} = [\begin{matrix} (B_{x} - A_{x}) \hat{i} + (B_{y} - A_{y}) \hat{j} + \\ (B_{z} - A_{z}) \hat{k} \end{matrix}]$
$\times [(C_{x} - B_{x}) \hat{i} + (C_{y} - B_{y}) \hat{j} + (C_{z} - B_{z}) \hat{k}]$
$= [x_{0} - d - x_{0} - d] \hat{i} + (a + a) \hat{j} + (- b + b) \hat{k}]$
$\times [(x_{0} - d - x_{0} + d) \hat{i} + (a - a) \hat{j} + (b + b) \hat{k}]$
$∴ \vec{s} = (- 2 d \hat{i} + 2 a \hat{j}) \times (2 b \hat{k}) = 4 b d \hat{j} + 4 a b \hat{i}$
$| \vec{m} | = I | \vec{S} |$
$= 4 I b \sqrt{a^{2} + d^{2}}$
$= 4 \times (0.03) (10) \sqrt{12^{2} + 5^{2}}$
$= 4 \times 0.3 \times 13 = 15.6 J T^{- 1}$

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