00. Biot-Savart's Law and Magnetic Field, Lorentz Force
Moving Charges & Magnetism

153200 Two wire loops $P Q R S P$ formed by joining two semicircle wires of radii $R_{1}$ and $R_{2}$ carrying a current $I$ as shown in figure. The magnetic field at centre $C$ is

1 $\frac{\mu_{0} \mathrm{I}}{4}\left(\frac{1}{\mathrm{R}_{1}}-\frac{1}{\mathrm{R}_{2}}\right)$
2 $\frac{\mu_{0} \mathrm{I}}{4}\left(\frac{1}{\mathrm{R}_{2}}-\frac{1}{\mathrm{R}_{1}}\right)$
3 $\frac{\mu_{0} \mathrm{I}}{2}\left(\frac{1}{\mathrm{R}_{1}}-\frac{1}{\mathrm{R}_{2}}\right)$
4 $\frac{\mu_{0} \mathrm{I}}{2}\left(\frac{1}{\mathrm{R}_{2}}-\frac{1}{\mathrm{R}_{1}}\right)$
Moving Charges & Magnetism

153202 A magnetic field of $5 \times 10^{-5} \mathrm{~T}$ is produced at a perpendicular distance of $0.2 \mathrm{~m}$ from a long straight wire carrying electric current. If the permeability of free space is $4 \pi \times 10^{-7} \mathrm{~T} \mathrm{~m} / \mathrm{A}$. The current passing through the wire in $A$ is

1 45
2 40
3 50
4 30
Moving Charges & Magnetism

153203 A long wire carries a current of $18 \mathrm{~A}$ kept along the axis of a long solenoid of radius $1 \mathrm{~cm}$. The field due to the solenoid is $8.0 \times 10^{-3} \mathrm{~T}$. The magnitude of the resultant field at a point 0.6 $\mathrm{mm}$ from the solenoid axis is (Assume, $\mu_{0}=4 \pi$ $\left.\times 10^{-7} \mathrm{Tm} / \mathrm{A}\right)$

1 $6 \times 10^{-3} \mathrm{~T}$
2 $6 \times 10^{-4} \mathrm{~T}$
3 $2 \sqrt{7} \times 10^{-3} \mathrm{~T}$
4 $10 \times 10^{-3} \mathrm{~T}$
Moving Charges & Magnetism

153204 A dielectric circular dise of radius $R$ carries a uniform surface charge density $\sigma$. If it rotates about its axis with angular velocity $\omega$, the magnetic field at the centre of disc is :

1 $\frac{\mu_{0} \sigma \omega R^{2}}{2 \pi}$
2 $\frac{\mu_{0} \sigma \omega R}{2}$
3 $\frac{\mu_{0} \sigma \omega R^{2}}{4}$
4 $\frac{\mu_{0} \sigma \omega R^{2}}{2 \sqrt{2}}$
Moving Charges & Magnetism

153205 A long straight wire carrying current $16 \mathrm{~A}$ is bent at $90^{\circ}$ such that half of the wire lies along the positive $x$-axis and other half lies along the positive $y$-axis. What is the magnitude of the magnetic field at the point, $r=(-2 \widehat{\mathbf{i}}+0 \widehat{\mathbf{j}}) \mathbf{m m}$ ?
$\text { (Assume, } \frac{\mu_{0}}{4 \pi}=10^{-7} \mathrm{H} \mathrm{m}^{-1} \text { ) }$

1 $1.2 \mathrm{mT}$
2 $0.8 \mathrm{mT}$
3 $3.2 \mathrm{mT}$
4 $1.6 \mathrm{mT}$
Moving Charges & Magnetism

153200 Two wire loops $P Q R S P$ formed by joining two semicircle wires of radii $R_{1}$ and $R_{2}$ carrying a current $I$ as shown in figure. The magnetic field at centre $C$ is

1 $\frac{\mu_{0} \mathrm{I}}{4}\left(\frac{1}{\mathrm{R}_{1}}-\frac{1}{\mathrm{R}_{2}}\right)$
2 $\frac{\mu_{0} \mathrm{I}}{4}\left(\frac{1}{\mathrm{R}_{2}}-\frac{1}{\mathrm{R}_{1}}\right)$
3 $\frac{\mu_{0} \mathrm{I}}{2}\left(\frac{1}{\mathrm{R}_{1}}-\frac{1}{\mathrm{R}_{2}}\right)$
4 $\frac{\mu_{0} \mathrm{I}}{2}\left(\frac{1}{\mathrm{R}_{2}}-\frac{1}{\mathrm{R}_{1}}\right)$
Moving Charges & Magnetism

153202 A magnetic field of $5 \times 10^{-5} \mathrm{~T}$ is produced at a perpendicular distance of $0.2 \mathrm{~m}$ from a long straight wire carrying electric current. If the permeability of free space is $4 \pi \times 10^{-7} \mathrm{~T} \mathrm{~m} / \mathrm{A}$. The current passing through the wire in $A$ is

1 45
2 40
3 50
4 30
Moving Charges & Magnetism

153203 A long wire carries a current of $18 \mathrm{~A}$ kept along the axis of a long solenoid of radius $1 \mathrm{~cm}$. The field due to the solenoid is $8.0 \times 10^{-3} \mathrm{~T}$. The magnitude of the resultant field at a point 0.6 $\mathrm{mm}$ from the solenoid axis is (Assume, $\mu_{0}=4 \pi$ $\left.\times 10^{-7} \mathrm{Tm} / \mathrm{A}\right)$

1 $6 \times 10^{-3} \mathrm{~T}$
2 $6 \times 10^{-4} \mathrm{~T}$
3 $2 \sqrt{7} \times 10^{-3} \mathrm{~T}$
4 $10 \times 10^{-3} \mathrm{~T}$
Moving Charges & Magnetism

153204 A dielectric circular dise of radius $R$ carries a uniform surface charge density $\sigma$. If it rotates about its axis with angular velocity $\omega$, the magnetic field at the centre of disc is :

1 $\frac{\mu_{0} \sigma \omega R^{2}}{2 \pi}$
2 $\frac{\mu_{0} \sigma \omega R}{2}$
3 $\frac{\mu_{0} \sigma \omega R^{2}}{4}$
4 $\frac{\mu_{0} \sigma \omega R^{2}}{2 \sqrt{2}}$
Moving Charges & Magnetism

153205 A long straight wire carrying current $16 \mathrm{~A}$ is bent at $90^{\circ}$ such that half of the wire lies along the positive $x$-axis and other half lies along the positive $y$-axis. What is the magnitude of the magnetic field at the point, $r=(-2 \widehat{\mathbf{i}}+0 \widehat{\mathbf{j}}) \mathbf{m m}$ ?
$\text { (Assume, } \frac{\mu_{0}}{4 \pi}=10^{-7} \mathrm{H} \mathrm{m}^{-1} \text { ) }$

1 $1.2 \mathrm{mT}$
2 $0.8 \mathrm{mT}$
3 $3.2 \mathrm{mT}$
4 $1.6 \mathrm{mT}$
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Moving Charges & Magnetism

153200 Two wire loops $P Q R S P$ formed by joining two semicircle wires of radii $R_{1}$ and $R_{2}$ carrying a current $I$ as shown in figure. The magnetic field at centre $C$ is

1 $\frac{\mu_{0} \mathrm{I}}{4}\left(\frac{1}{\mathrm{R}_{1}}-\frac{1}{\mathrm{R}_{2}}\right)$
2 $\frac{\mu_{0} \mathrm{I}}{4}\left(\frac{1}{\mathrm{R}_{2}}-\frac{1}{\mathrm{R}_{1}}\right)$
3 $\frac{\mu_{0} \mathrm{I}}{2}\left(\frac{1}{\mathrm{R}_{1}}-\frac{1}{\mathrm{R}_{2}}\right)$
4 $\frac{\mu_{0} \mathrm{I}}{2}\left(\frac{1}{\mathrm{R}_{2}}-\frac{1}{\mathrm{R}_{1}}\right)$
Moving Charges & Magnetism

153202 A magnetic field of $5 \times 10^{-5} \mathrm{~T}$ is produced at a perpendicular distance of $0.2 \mathrm{~m}$ from a long straight wire carrying electric current. If the permeability of free space is $4 \pi \times 10^{-7} \mathrm{~T} \mathrm{~m} / \mathrm{A}$. The current passing through the wire in $A$ is

1 45
2 40
3 50
4 30
Moving Charges & Magnetism

153203 A long wire carries a current of $18 \mathrm{~A}$ kept along the axis of a long solenoid of radius $1 \mathrm{~cm}$. The field due to the solenoid is $8.0 \times 10^{-3} \mathrm{~T}$. The magnitude of the resultant field at a point 0.6 $\mathrm{mm}$ from the solenoid axis is (Assume, $\mu_{0}=4 \pi$ $\left.\times 10^{-7} \mathrm{Tm} / \mathrm{A}\right)$

1 $6 \times 10^{-3} \mathrm{~T}$
2 $6 \times 10^{-4} \mathrm{~T}$
3 $2 \sqrt{7} \times 10^{-3} \mathrm{~T}$
4 $10 \times 10^{-3} \mathrm{~T}$
Moving Charges & Magnetism

153204 A dielectric circular dise of radius $R$ carries a uniform surface charge density $\sigma$. If it rotates about its axis with angular velocity $\omega$, the magnetic field at the centre of disc is :

1 $\frac{\mu_{0} \sigma \omega R^{2}}{2 \pi}$
2 $\frac{\mu_{0} \sigma \omega R}{2}$
3 $\frac{\mu_{0} \sigma \omega R^{2}}{4}$
4 $\frac{\mu_{0} \sigma \omega R^{2}}{2 \sqrt{2}}$
Moving Charges & Magnetism

153205 A long straight wire carrying current $16 \mathrm{~A}$ is bent at $90^{\circ}$ such that half of the wire lies along the positive $x$-axis and other half lies along the positive $y$-axis. What is the magnitude of the magnetic field at the point, $r=(-2 \widehat{\mathbf{i}}+0 \widehat{\mathbf{j}}) \mathbf{m m}$ ?
$\text { (Assume, } \frac{\mu_{0}}{4 \pi}=10^{-7} \mathrm{H} \mathrm{m}^{-1} \text { ) }$

1 $1.2 \mathrm{mT}$
2 $0.8 \mathrm{mT}$
3 $3.2 \mathrm{mT}$
4 $1.6 \mathrm{mT}$
Moving Charges & Magnetism

153200 Two wire loops $P Q R S P$ formed by joining two semicircle wires of radii $R_{1}$ and $R_{2}$ carrying a current $I$ as shown in figure. The magnetic field at centre $C$ is

1 $\frac{\mu_{0} \mathrm{I}}{4}\left(\frac{1}{\mathrm{R}_{1}}-\frac{1}{\mathrm{R}_{2}}\right)$
2 $\frac{\mu_{0} \mathrm{I}}{4}\left(\frac{1}{\mathrm{R}_{2}}-\frac{1}{\mathrm{R}_{1}}\right)$
3 $\frac{\mu_{0} \mathrm{I}}{2}\left(\frac{1}{\mathrm{R}_{1}}-\frac{1}{\mathrm{R}_{2}}\right)$
4 $\frac{\mu_{0} \mathrm{I}}{2}\left(\frac{1}{\mathrm{R}_{2}}-\frac{1}{\mathrm{R}_{1}}\right)$
Moving Charges & Magnetism

153202 A magnetic field of $5 \times 10^{-5} \mathrm{~T}$ is produced at a perpendicular distance of $0.2 \mathrm{~m}$ from a long straight wire carrying electric current. If the permeability of free space is $4 \pi \times 10^{-7} \mathrm{~T} \mathrm{~m} / \mathrm{A}$. The current passing through the wire in $A$ is

1 45
2 40
3 50
4 30
Moving Charges & Magnetism

153203 A long wire carries a current of $18 \mathrm{~A}$ kept along the axis of a long solenoid of radius $1 \mathrm{~cm}$. The field due to the solenoid is $8.0 \times 10^{-3} \mathrm{~T}$. The magnitude of the resultant field at a point 0.6 $\mathrm{mm}$ from the solenoid axis is (Assume, $\mu_{0}=4 \pi$ $\left.\times 10^{-7} \mathrm{Tm} / \mathrm{A}\right)$

1 $6 \times 10^{-3} \mathrm{~T}$
2 $6 \times 10^{-4} \mathrm{~T}$
3 $2 \sqrt{7} \times 10^{-3} \mathrm{~T}$
4 $10 \times 10^{-3} \mathrm{~T}$
Moving Charges & Magnetism

153204 A dielectric circular dise of radius $R$ carries a uniform surface charge density $\sigma$. If it rotates about its axis with angular velocity $\omega$, the magnetic field at the centre of disc is :

1 $\frac{\mu_{0} \sigma \omega R^{2}}{2 \pi}$
2 $\frac{\mu_{0} \sigma \omega R}{2}$
3 $\frac{\mu_{0} \sigma \omega R^{2}}{4}$
4 $\frac{\mu_{0} \sigma \omega R^{2}}{2 \sqrt{2}}$
Moving Charges & Magnetism

153205 A long straight wire carrying current $16 \mathrm{~A}$ is bent at $90^{\circ}$ such that half of the wire lies along the positive $x$-axis and other half lies along the positive $y$-axis. What is the magnitude of the magnetic field at the point, $r=(-2 \widehat{\mathbf{i}}+0 \widehat{\mathbf{j}}) \mathbf{m m}$ ?
$\text { (Assume, } \frac{\mu_{0}}{4 \pi}=10^{-7} \mathrm{H} \mathrm{m}^{-1} \text { ) }$

1 $1.2 \mathrm{mT}$
2 $0.8 \mathrm{mT}$
3 $3.2 \mathrm{mT}$
4 $1.6 \mathrm{mT}$
Moving Charges & Magnetism

153200 Two wire loops $P Q R S P$ formed by joining two semicircle wires of radii $R_{1}$ and $R_{2}$ carrying a current $I$ as shown in figure. The magnetic field at centre $C$ is

1 $\frac{\mu_{0} \mathrm{I}}{4}\left(\frac{1}{\mathrm{R}_{1}}-\frac{1}{\mathrm{R}_{2}}\right)$
2 $\frac{\mu_{0} \mathrm{I}}{4}\left(\frac{1}{\mathrm{R}_{2}}-\frac{1}{\mathrm{R}_{1}}\right)$
3 $\frac{\mu_{0} \mathrm{I}}{2}\left(\frac{1}{\mathrm{R}_{1}}-\frac{1}{\mathrm{R}_{2}}\right)$
4 $\frac{\mu_{0} \mathrm{I}}{2}\left(\frac{1}{\mathrm{R}_{2}}-\frac{1}{\mathrm{R}_{1}}\right)$
Moving Charges & Magnetism

153202 A magnetic field of $5 \times 10^{-5} \mathrm{~T}$ is produced at a perpendicular distance of $0.2 \mathrm{~m}$ from a long straight wire carrying electric current. If the permeability of free space is $4 \pi \times 10^{-7} \mathrm{~T} \mathrm{~m} / \mathrm{A}$. The current passing through the wire in $A$ is

1 45
2 40
3 50
4 30
Moving Charges & Magnetism

153203 A long wire carries a current of $18 \mathrm{~A}$ kept along the axis of a long solenoid of radius $1 \mathrm{~cm}$. The field due to the solenoid is $8.0 \times 10^{-3} \mathrm{~T}$. The magnitude of the resultant field at a point 0.6 $\mathrm{mm}$ from the solenoid axis is (Assume, $\mu_{0}=4 \pi$ $\left.\times 10^{-7} \mathrm{Tm} / \mathrm{A}\right)$

1 $6 \times 10^{-3} \mathrm{~T}$
2 $6 \times 10^{-4} \mathrm{~T}$
3 $2 \sqrt{7} \times 10^{-3} \mathrm{~T}$
4 $10 \times 10^{-3} \mathrm{~T}$
Moving Charges & Magnetism

153204 A dielectric circular dise of radius $R$ carries a uniform surface charge density $\sigma$. If it rotates about its axis with angular velocity $\omega$, the magnetic field at the centre of disc is :

1 $\frac{\mu_{0} \sigma \omega R^{2}}{2 \pi}$
2 $\frac{\mu_{0} \sigma \omega R}{2}$
3 $\frac{\mu_{0} \sigma \omega R^{2}}{4}$
4 $\frac{\mu_{0} \sigma \omega R^{2}}{2 \sqrt{2}}$
Moving Charges & Magnetism

153205 A long straight wire carrying current $16 \mathrm{~A}$ is bent at $90^{\circ}$ such that half of the wire lies along the positive $x$-axis and other half lies along the positive $y$-axis. What is the magnitude of the magnetic field at the point, $r=(-2 \widehat{\mathbf{i}}+0 \widehat{\mathbf{j}}) \mathbf{m m}$ ?
$\text { (Assume, } \frac{\mu_{0}}{4 \pi}=10^{-7} \mathrm{H} \mathrm{m}^{-1} \text { ) }$

1 $1.2 \mathrm{mT}$
2 $0.8 \mathrm{mT}$
3 $3.2 \mathrm{mT}$
4 $1.6 \mathrm{mT}$