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

153359 The magnetic induction at a point $P$ which is at the distance of $4 \mathrm{~cm}$ from a long current carrying wire is $10^{-3} \mathrm{~T}$. The field of induction at a distance $12 \mathrm{~cm}$ from the current will be

1 $3.33 \times 10^{-4} \mathrm{~T}$
2 $1.11 \times 10^{-4} \mathrm{~T}$
3 $3 \times 10^{-3} \mathrm{~T}$
4 $9 \times 10^{-3} \mathrm{~T}$
Moving Charges & Magnetism

153361 Two identical long conducting wires $\mathrm{AOB}$ and COD are placed at right angle to each other, such that one is above the other and $O$ is their common point. The wires carry $I_{1}$ and $I_{2}$ currents, respectively. Point $P$ is lying at distanced from $O$ along a direction perpendicular to the plane containing the wires. The magnetic field at the point $P$ will be

1 $\frac{\mu_{0}}{2 \pi \mathrm{d}}\left(\frac{\mathrm{I}_{1}}{\mathrm{I}_{2}}\right)$
2 $\frac{\mu_{0}}{2 \pi \mathrm{d}}\left(\mathrm{I}_{1}+\mathrm{I}_{2}\right)$
3 $\frac{\mu_{0}}{2 \pi d}\left(I_{1}^{2}-I_{2}^{2}\right)$
4 $\frac{\mu_{0}}{2 \pi d}\left(I_{1}^{2}+I_{2}^{2}\right)^{1 / 2}$
Moving Charges & Magnetism

153363 A current carrying thin uniform wire of length $' 4 l '$ is bent like a square so that it produces a magnetic induction $B_{1}$ at the centre of the square. When the same wire is bent like a circle, it produces a magnetic induction $B_{2}$ at the centre of the circle. The ratio between $B_{1}$ and $B_{2}$ is

1 $\pi^{2}: 8 \sqrt{2}$
2 $8: \pi^{2}$
3 $\sqrt{2}: \pi^{2}$
4 $8 \sqrt{2}: \pi^{2}$
Moving Charges & Magnetism

153364 A pair of stationary and infinitely long bent wires are placed in the $x-y$ plane as shown in the figure. The two wires carry currents of $4 \mathrm{~A}$ and $9 \mathrm{~A}$ respectively. If the segments $D$ and $A$ are along the $x$-axis and the segments $C$ and $F$ are parallel to $\mathrm{y}$-axis such that $\mathrm{OB}=\mathbf{2} \mathrm{cm}$ and $O E=3 \mathrm{~cm}$, then the magnitude of the magnetic induction at the origin ' $O$ ' is $\left(\mu_{0}=4 \pi \times 10^{-7} \mathrm{Hm}^{-1}\right)$

1 $4 \times 10^{-5} \mathrm{~T}$
2 $5 \times 10^{-5} \mathrm{~T}$
3 $6 \times 10^{-5} \mathrm{~T}$
4 $2 \times 10^{-5} \mathrm{~T}$
Moving Charges & Magnetism

153365 A magnetic dipole is placed under the effect of two magnetic fields inclined at $75^{\circ}$ to each other. One of the field has a magnetic induction of $1.5 \times 10^{-2} \mathrm{~T}$. The magnet comes to rest at an angle of $30^{\circ}$ with the direction of this field. The magnitude of the other field is

1 $1.5 \times 10^{-2} \mathrm{~T}$
2 $1.5 \sqrt{2} \times 10^{-2} \mathrm{~T}$
3 $\frac{1.5}{\sqrt{2}} \times 10^{-2} \mathrm{~T}$
4 $\frac{1.5}{2 \sqrt{2}} \times 10^{-2} \mathrm{~T}$
Moving Charges & Magnetism

153359 The magnetic induction at a point $P$ which is at the distance of $4 \mathrm{~cm}$ from a long current carrying wire is $10^{-3} \mathrm{~T}$. The field of induction at a distance $12 \mathrm{~cm}$ from the current will be

1 $3.33 \times 10^{-4} \mathrm{~T}$
2 $1.11 \times 10^{-4} \mathrm{~T}$
3 $3 \times 10^{-3} \mathrm{~T}$
4 $9 \times 10^{-3} \mathrm{~T}$
Moving Charges & Magnetism

153361 Two identical long conducting wires $\mathrm{AOB}$ and COD are placed at right angle to each other, such that one is above the other and $O$ is their common point. The wires carry $I_{1}$ and $I_{2}$ currents, respectively. Point $P$ is lying at distanced from $O$ along a direction perpendicular to the plane containing the wires. The magnetic field at the point $P$ will be

1 $\frac{\mu_{0}}{2 \pi \mathrm{d}}\left(\frac{\mathrm{I}_{1}}{\mathrm{I}_{2}}\right)$
2 $\frac{\mu_{0}}{2 \pi \mathrm{d}}\left(\mathrm{I}_{1}+\mathrm{I}_{2}\right)$
3 $\frac{\mu_{0}}{2 \pi d}\left(I_{1}^{2}-I_{2}^{2}\right)$
4 $\frac{\mu_{0}}{2 \pi d}\left(I_{1}^{2}+I_{2}^{2}\right)^{1 / 2}$
Moving Charges & Magnetism

153363 A current carrying thin uniform wire of length $' 4 l '$ is bent like a square so that it produces a magnetic induction $B_{1}$ at the centre of the square. When the same wire is bent like a circle, it produces a magnetic induction $B_{2}$ at the centre of the circle. The ratio between $B_{1}$ and $B_{2}$ is

1 $\pi^{2}: 8 \sqrt{2}$
2 $8: \pi^{2}$
3 $\sqrt{2}: \pi^{2}$
4 $8 \sqrt{2}: \pi^{2}$
Moving Charges & Magnetism

153364 A pair of stationary and infinitely long bent wires are placed in the $x-y$ plane as shown in the figure. The two wires carry currents of $4 \mathrm{~A}$ and $9 \mathrm{~A}$ respectively. If the segments $D$ and $A$ are along the $x$-axis and the segments $C$ and $F$ are parallel to $\mathrm{y}$-axis such that $\mathrm{OB}=\mathbf{2} \mathrm{cm}$ and $O E=3 \mathrm{~cm}$, then the magnitude of the magnetic induction at the origin ' $O$ ' is $\left(\mu_{0}=4 \pi \times 10^{-7} \mathrm{Hm}^{-1}\right)$

1 $4 \times 10^{-5} \mathrm{~T}$
2 $5 \times 10^{-5} \mathrm{~T}$
3 $6 \times 10^{-5} \mathrm{~T}$
4 $2 \times 10^{-5} \mathrm{~T}$
Moving Charges & Magnetism

153365 A magnetic dipole is placed under the effect of two magnetic fields inclined at $75^{\circ}$ to each other. One of the field has a magnetic induction of $1.5 \times 10^{-2} \mathrm{~T}$. The magnet comes to rest at an angle of $30^{\circ}$ with the direction of this field. The magnitude of the other field is

1 $1.5 \times 10^{-2} \mathrm{~T}$
2 $1.5 \sqrt{2} \times 10^{-2} \mathrm{~T}$
3 $\frac{1.5}{\sqrt{2}} \times 10^{-2} \mathrm{~T}$
4 $\frac{1.5}{2 \sqrt{2}} \times 10^{-2} \mathrm{~T}$
Moving Charges & Magnetism

153359 The magnetic induction at a point $P$ which is at the distance of $4 \mathrm{~cm}$ from a long current carrying wire is $10^{-3} \mathrm{~T}$. The field of induction at a distance $12 \mathrm{~cm}$ from the current will be

1 $3.33 \times 10^{-4} \mathrm{~T}$
2 $1.11 \times 10^{-4} \mathrm{~T}$
3 $3 \times 10^{-3} \mathrm{~T}$
4 $9 \times 10^{-3} \mathrm{~T}$
Moving Charges & Magnetism

153361 Two identical long conducting wires $\mathrm{AOB}$ and COD are placed at right angle to each other, such that one is above the other and $O$ is their common point. The wires carry $I_{1}$ and $I_{2}$ currents, respectively. Point $P$ is lying at distanced from $O$ along a direction perpendicular to the plane containing the wires. The magnetic field at the point $P$ will be

1 $\frac{\mu_{0}}{2 \pi \mathrm{d}}\left(\frac{\mathrm{I}_{1}}{\mathrm{I}_{2}}\right)$
2 $\frac{\mu_{0}}{2 \pi \mathrm{d}}\left(\mathrm{I}_{1}+\mathrm{I}_{2}\right)$
3 $\frac{\mu_{0}}{2 \pi d}\left(I_{1}^{2}-I_{2}^{2}\right)$
4 $\frac{\mu_{0}}{2 \pi d}\left(I_{1}^{2}+I_{2}^{2}\right)^{1 / 2}$
Moving Charges & Magnetism

153363 A current carrying thin uniform wire of length $' 4 l '$ is bent like a square so that it produces a magnetic induction $B_{1}$ at the centre of the square. When the same wire is bent like a circle, it produces a magnetic induction $B_{2}$ at the centre of the circle. The ratio between $B_{1}$ and $B_{2}$ is

1 $\pi^{2}: 8 \sqrt{2}$
2 $8: \pi^{2}$
3 $\sqrt{2}: \pi^{2}$
4 $8 \sqrt{2}: \pi^{2}$
Moving Charges & Magnetism

153364 A pair of stationary and infinitely long bent wires are placed in the $x-y$ plane as shown in the figure. The two wires carry currents of $4 \mathrm{~A}$ and $9 \mathrm{~A}$ respectively. If the segments $D$ and $A$ are along the $x$-axis and the segments $C$ and $F$ are parallel to $\mathrm{y}$-axis such that $\mathrm{OB}=\mathbf{2} \mathrm{cm}$ and $O E=3 \mathrm{~cm}$, then the magnitude of the magnetic induction at the origin ' $O$ ' is $\left(\mu_{0}=4 \pi \times 10^{-7} \mathrm{Hm}^{-1}\right)$

1 $4 \times 10^{-5} \mathrm{~T}$
2 $5 \times 10^{-5} \mathrm{~T}$
3 $6 \times 10^{-5} \mathrm{~T}$
4 $2 \times 10^{-5} \mathrm{~T}$
Moving Charges & Magnetism

153365 A magnetic dipole is placed under the effect of two magnetic fields inclined at $75^{\circ}$ to each other. One of the field has a magnetic induction of $1.5 \times 10^{-2} \mathrm{~T}$. The magnet comes to rest at an angle of $30^{\circ}$ with the direction of this field. The magnitude of the other field is

1 $1.5 \times 10^{-2} \mathrm{~T}$
2 $1.5 \sqrt{2} \times 10^{-2} \mathrm{~T}$
3 $\frac{1.5}{\sqrt{2}} \times 10^{-2} \mathrm{~T}$
4 $\frac{1.5}{2 \sqrt{2}} \times 10^{-2} \mathrm{~T}$
Moving Charges & Magnetism

153359 The magnetic induction at a point $P$ which is at the distance of $4 \mathrm{~cm}$ from a long current carrying wire is $10^{-3} \mathrm{~T}$. The field of induction at a distance $12 \mathrm{~cm}$ from the current will be

1 $3.33 \times 10^{-4} \mathrm{~T}$
2 $1.11 \times 10^{-4} \mathrm{~T}$
3 $3 \times 10^{-3} \mathrm{~T}$
4 $9 \times 10^{-3} \mathrm{~T}$
Moving Charges & Magnetism

153361 Two identical long conducting wires $\mathrm{AOB}$ and COD are placed at right angle to each other, such that one is above the other and $O$ is their common point. The wires carry $I_{1}$ and $I_{2}$ currents, respectively. Point $P$ is lying at distanced from $O$ along a direction perpendicular to the plane containing the wires. The magnetic field at the point $P$ will be

1 $\frac{\mu_{0}}{2 \pi \mathrm{d}}\left(\frac{\mathrm{I}_{1}}{\mathrm{I}_{2}}\right)$
2 $\frac{\mu_{0}}{2 \pi \mathrm{d}}\left(\mathrm{I}_{1}+\mathrm{I}_{2}\right)$
3 $\frac{\mu_{0}}{2 \pi d}\left(I_{1}^{2}-I_{2}^{2}\right)$
4 $\frac{\mu_{0}}{2 \pi d}\left(I_{1}^{2}+I_{2}^{2}\right)^{1 / 2}$
Moving Charges & Magnetism

153363 A current carrying thin uniform wire of length $' 4 l '$ is bent like a square so that it produces a magnetic induction $B_{1}$ at the centre of the square. When the same wire is bent like a circle, it produces a magnetic induction $B_{2}$ at the centre of the circle. The ratio between $B_{1}$ and $B_{2}$ is

1 $\pi^{2}: 8 \sqrt{2}$
2 $8: \pi^{2}$
3 $\sqrt{2}: \pi^{2}$
4 $8 \sqrt{2}: \pi^{2}$
Moving Charges & Magnetism

153364 A pair of stationary and infinitely long bent wires are placed in the $x-y$ plane as shown in the figure. The two wires carry currents of $4 \mathrm{~A}$ and $9 \mathrm{~A}$ respectively. If the segments $D$ and $A$ are along the $x$-axis and the segments $C$ and $F$ are parallel to $\mathrm{y}$-axis such that $\mathrm{OB}=\mathbf{2} \mathrm{cm}$ and $O E=3 \mathrm{~cm}$, then the magnitude of the magnetic induction at the origin ' $O$ ' is $\left(\mu_{0}=4 \pi \times 10^{-7} \mathrm{Hm}^{-1}\right)$

1 $4 \times 10^{-5} \mathrm{~T}$
2 $5 \times 10^{-5} \mathrm{~T}$
3 $6 \times 10^{-5} \mathrm{~T}$
4 $2 \times 10^{-5} \mathrm{~T}$
Moving Charges & Magnetism

153365 A magnetic dipole is placed under the effect of two magnetic fields inclined at $75^{\circ}$ to each other. One of the field has a magnetic induction of $1.5 \times 10^{-2} \mathrm{~T}$. The magnet comes to rest at an angle of $30^{\circ}$ with the direction of this field. The magnitude of the other field is

1 $1.5 \times 10^{-2} \mathrm{~T}$
2 $1.5 \sqrt{2} \times 10^{-2} \mathrm{~T}$
3 $\frac{1.5}{\sqrt{2}} \times 10^{-2} \mathrm{~T}$
4 $\frac{1.5}{2 \sqrt{2}} \times 10^{-2} \mathrm{~T}$
Moving Charges & Magnetism

153359 The magnetic induction at a point $P$ which is at the distance of $4 \mathrm{~cm}$ from a long current carrying wire is $10^{-3} \mathrm{~T}$. The field of induction at a distance $12 \mathrm{~cm}$ from the current will be

1 $3.33 \times 10^{-4} \mathrm{~T}$
2 $1.11 \times 10^{-4} \mathrm{~T}$
3 $3 \times 10^{-3} \mathrm{~T}$
4 $9 \times 10^{-3} \mathrm{~T}$
Moving Charges & Magnetism

153361 Two identical long conducting wires $\mathrm{AOB}$ and COD are placed at right angle to each other, such that one is above the other and $O$ is their common point. The wires carry $I_{1}$ and $I_{2}$ currents, respectively. Point $P$ is lying at distanced from $O$ along a direction perpendicular to the plane containing the wires. The magnetic field at the point $P$ will be

1 $\frac{\mu_{0}}{2 \pi \mathrm{d}}\left(\frac{\mathrm{I}_{1}}{\mathrm{I}_{2}}\right)$
2 $\frac{\mu_{0}}{2 \pi \mathrm{d}}\left(\mathrm{I}_{1}+\mathrm{I}_{2}\right)$
3 $\frac{\mu_{0}}{2 \pi d}\left(I_{1}^{2}-I_{2}^{2}\right)$
4 $\frac{\mu_{0}}{2 \pi d}\left(I_{1}^{2}+I_{2}^{2}\right)^{1 / 2}$
Moving Charges & Magnetism

153363 A current carrying thin uniform wire of length $' 4 l '$ is bent like a square so that it produces a magnetic induction $B_{1}$ at the centre of the square. When the same wire is bent like a circle, it produces a magnetic induction $B_{2}$ at the centre of the circle. The ratio between $B_{1}$ and $B_{2}$ is

1 $\pi^{2}: 8 \sqrt{2}$
2 $8: \pi^{2}$
3 $\sqrt{2}: \pi^{2}$
4 $8 \sqrt{2}: \pi^{2}$
Moving Charges & Magnetism

153364 A pair of stationary and infinitely long bent wires are placed in the $x-y$ plane as shown in the figure. The two wires carry currents of $4 \mathrm{~A}$ and $9 \mathrm{~A}$ respectively. If the segments $D$ and $A$ are along the $x$-axis and the segments $C$ and $F$ are parallel to $\mathrm{y}$-axis such that $\mathrm{OB}=\mathbf{2} \mathrm{cm}$ and $O E=3 \mathrm{~cm}$, then the magnitude of the magnetic induction at the origin ' $O$ ' is $\left(\mu_{0}=4 \pi \times 10^{-7} \mathrm{Hm}^{-1}\right)$

1 $4 \times 10^{-5} \mathrm{~T}$
2 $5 \times 10^{-5} \mathrm{~T}$
3 $6 \times 10^{-5} \mathrm{~T}$
4 $2 \times 10^{-5} \mathrm{~T}$
Moving Charges & Magnetism

153365 A magnetic dipole is placed under the effect of two magnetic fields inclined at $75^{\circ}$ to each other. One of the field has a magnetic induction of $1.5 \times 10^{-2} \mathrm{~T}$. The magnet comes to rest at an angle of $30^{\circ}$ with the direction of this field. The magnitude of the other field is

1 $1.5 \times 10^{-2} \mathrm{~T}$
2 $1.5 \sqrt{2} \times 10^{-2} \mathrm{~T}$
3 $\frac{1.5}{\sqrt{2}} \times 10^{-2} \mathrm{~T}$
4 $\frac{1.5}{2 \sqrt{2}} \times 10^{-2} \mathrm{~T}$