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

153222 Two short bar magnets each of magnetic moment of $9 \mathrm{Am}^{2}$ are placed such that one is at $x=-3 \mathrm{~cm}$ and the other at $y=-3 \mathrm{~cm}$. If their magnetic moments are directed along positive and negative $X$-directions respectively, then the resultant magnetic field at the origin is

1 $100 \mathrm{~T}$
2 $10 \mathrm{~T}$
3 $0.1 \mathrm{~T}$
4 $0.001 \mathrm{~T}$
Moving Charges & Magnetism

153223 Two infinitely long wires carry currents $4 \mathrm{~A}$ and $3 A$ placed along $X$-axis and $Y$-axis respectively. Magnetic field at a point $P(0,0, d)$ m will be ...... T.

1 $\frac{4 \mu_{0}}{2 \pi d}$
2 $\frac{3 \mu_{0}}{2 \pi d}$
3 $\frac{7 \mu_{0}}{2 \pi \mathrm{d}}$
4 $\frac{5 \mu_{0}}{2 \pi \mathrm{d}}$
Moving Charges & Magnetism

153226 A bar magnet of magnetic moment $M$ is placed at a distance $D$ with its axis along positive $X$ axis. Likewise, second bar magnet of magnetic moment $M$ is placed at a distance $2 D$ on positive $\mathrm{Y}$-axis and perpendicular to it as shown in the figure. The magnitude of magnetic field at the origin is $|B|=\alpha\left[\frac{\mu_{0}}{4 \pi} \frac{M}{D^{3}}\right]$.
The value of $\alpha$ must be (assume $\mathrm{D}>>l$, where $l$ is the length of magnets)

1 2
2 $\frac{15}{8}$
3 $\frac{17}{8}$
4 $\frac{9}{8}$
Moving Charges & Magnetism

153227 A steady current I flows through a wire with one end at $O$ and the other end extending upto infinity as shown in the figure. The magnetic field at a point $P$, located at a distance $d$ from $O$ is

1 $\frac{\mu_{0} I}{4 \pi d \cos \alpha}(1-\sin \alpha)$
2 $\frac{\mu_{0} I}{2 \pi d \cos \alpha}(1-\sin \alpha)$
3 $\frac{\mu_{0} I}{4 \pi \mathrm{d}}$
4 $\frac{\mu_{0} \mathrm{I}}{4 \pi \mathrm{d} \sin \alpha}(1-\cos \alpha)$
Moving Charges & Magnetism

153228 Consider a current carrying wire shown in the figure. If the radius of the curved part of the wire is $R$ and the linear parts are assumed to be very long, then the magnetic induction of the field at the point $O$ is

1 $\frac{\mu_{0}}{4 \pi} \frac{\mathrm{i}}{\mathrm{R}}(2+\pi)$
2 $\frac{\mu_{0} \mathrm{i}}{2 \pi \mathrm{R}}$
3 $\frac{\mu_{0}}{2} \frac{\mathrm{i}}{\mathrm{R}}$
4 $\frac{\mu_{0}}{4} \frac{\mathrm{i}}{\mathrm{R}}$
Moving Charges & Magnetism

153222 Two short bar magnets each of magnetic moment of $9 \mathrm{Am}^{2}$ are placed such that one is at $x=-3 \mathrm{~cm}$ and the other at $y=-3 \mathrm{~cm}$. If their magnetic moments are directed along positive and negative $X$-directions respectively, then the resultant magnetic field at the origin is

1 $100 \mathrm{~T}$
2 $10 \mathrm{~T}$
3 $0.1 \mathrm{~T}$
4 $0.001 \mathrm{~T}$
Moving Charges & Magnetism

153223 Two infinitely long wires carry currents $4 \mathrm{~A}$ and $3 A$ placed along $X$-axis and $Y$-axis respectively. Magnetic field at a point $P(0,0, d)$ m will be ...... T.

1 $\frac{4 \mu_{0}}{2 \pi d}$
2 $\frac{3 \mu_{0}}{2 \pi d}$
3 $\frac{7 \mu_{0}}{2 \pi \mathrm{d}}$
4 $\frac{5 \mu_{0}}{2 \pi \mathrm{d}}$
Moving Charges & Magnetism

153226 A bar magnet of magnetic moment $M$ is placed at a distance $D$ with its axis along positive $X$ axis. Likewise, second bar magnet of magnetic moment $M$ is placed at a distance $2 D$ on positive $\mathrm{Y}$-axis and perpendicular to it as shown in the figure. The magnitude of magnetic field at the origin is $|B|=\alpha\left[\frac{\mu_{0}}{4 \pi} \frac{M}{D^{3}}\right]$.
The value of $\alpha$ must be (assume $\mathrm{D}>>l$, where $l$ is the length of magnets)

1 2
2 $\frac{15}{8}$
3 $\frac{17}{8}$
4 $\frac{9}{8}$
Moving Charges & Magnetism

153227 A steady current I flows through a wire with one end at $O$ and the other end extending upto infinity as shown in the figure. The magnetic field at a point $P$, located at a distance $d$ from $O$ is

1 $\frac{\mu_{0} I}{4 \pi d \cos \alpha}(1-\sin \alpha)$
2 $\frac{\mu_{0} I}{2 \pi d \cos \alpha}(1-\sin \alpha)$
3 $\frac{\mu_{0} I}{4 \pi \mathrm{d}}$
4 $\frac{\mu_{0} \mathrm{I}}{4 \pi \mathrm{d} \sin \alpha}(1-\cos \alpha)$
Moving Charges & Magnetism

153228 Consider a current carrying wire shown in the figure. If the radius of the curved part of the wire is $R$ and the linear parts are assumed to be very long, then the magnetic induction of the field at the point $O$ is

1 $\frac{\mu_{0}}{4 \pi} \frac{\mathrm{i}}{\mathrm{R}}(2+\pi)$
2 $\frac{\mu_{0} \mathrm{i}}{2 \pi \mathrm{R}}$
3 $\frac{\mu_{0}}{2} \frac{\mathrm{i}}{\mathrm{R}}$
4 $\frac{\mu_{0}}{4} \frac{\mathrm{i}}{\mathrm{R}}$
Moving Charges & Magnetism

153222 Two short bar magnets each of magnetic moment of $9 \mathrm{Am}^{2}$ are placed such that one is at $x=-3 \mathrm{~cm}$ and the other at $y=-3 \mathrm{~cm}$. If their magnetic moments are directed along positive and negative $X$-directions respectively, then the resultant magnetic field at the origin is

1 $100 \mathrm{~T}$
2 $10 \mathrm{~T}$
3 $0.1 \mathrm{~T}$
4 $0.001 \mathrm{~T}$
Moving Charges & Magnetism

153223 Two infinitely long wires carry currents $4 \mathrm{~A}$ and $3 A$ placed along $X$-axis and $Y$-axis respectively. Magnetic field at a point $P(0,0, d)$ m will be ...... T.

1 $\frac{4 \mu_{0}}{2 \pi d}$
2 $\frac{3 \mu_{0}}{2 \pi d}$
3 $\frac{7 \mu_{0}}{2 \pi \mathrm{d}}$
4 $\frac{5 \mu_{0}}{2 \pi \mathrm{d}}$
Moving Charges & Magnetism

153226 A bar magnet of magnetic moment $M$ is placed at a distance $D$ with its axis along positive $X$ axis. Likewise, second bar magnet of magnetic moment $M$ is placed at a distance $2 D$ on positive $\mathrm{Y}$-axis and perpendicular to it as shown in the figure. The magnitude of magnetic field at the origin is $|B|=\alpha\left[\frac{\mu_{0}}{4 \pi} \frac{M}{D^{3}}\right]$.
The value of $\alpha$ must be (assume $\mathrm{D}>>l$, where $l$ is the length of magnets)

1 2
2 $\frac{15}{8}$
3 $\frac{17}{8}$
4 $\frac{9}{8}$
Moving Charges & Magnetism

153227 A steady current I flows through a wire with one end at $O$ and the other end extending upto infinity as shown in the figure. The magnetic field at a point $P$, located at a distance $d$ from $O$ is

1 $\frac{\mu_{0} I}{4 \pi d \cos \alpha}(1-\sin \alpha)$
2 $\frac{\mu_{0} I}{2 \pi d \cos \alpha}(1-\sin \alpha)$
3 $\frac{\mu_{0} I}{4 \pi \mathrm{d}}$
4 $\frac{\mu_{0} \mathrm{I}}{4 \pi \mathrm{d} \sin \alpha}(1-\cos \alpha)$
Moving Charges & Magnetism

153228 Consider a current carrying wire shown in the figure. If the radius of the curved part of the wire is $R$ and the linear parts are assumed to be very long, then the magnetic induction of the field at the point $O$ is

1 $\frac{\mu_{0}}{4 \pi} \frac{\mathrm{i}}{\mathrm{R}}(2+\pi)$
2 $\frac{\mu_{0} \mathrm{i}}{2 \pi \mathrm{R}}$
3 $\frac{\mu_{0}}{2} \frac{\mathrm{i}}{\mathrm{R}}$
4 $\frac{\mu_{0}}{4} \frac{\mathrm{i}}{\mathrm{R}}$
Moving Charges & Magnetism

153222 Two short bar magnets each of magnetic moment of $9 \mathrm{Am}^{2}$ are placed such that one is at $x=-3 \mathrm{~cm}$ and the other at $y=-3 \mathrm{~cm}$. If their magnetic moments are directed along positive and negative $X$-directions respectively, then the resultant magnetic field at the origin is

1 $100 \mathrm{~T}$
2 $10 \mathrm{~T}$
3 $0.1 \mathrm{~T}$
4 $0.001 \mathrm{~T}$
Moving Charges & Magnetism

153223 Two infinitely long wires carry currents $4 \mathrm{~A}$ and $3 A$ placed along $X$-axis and $Y$-axis respectively. Magnetic field at a point $P(0,0, d)$ m will be ...... T.

1 $\frac{4 \mu_{0}}{2 \pi d}$
2 $\frac{3 \mu_{0}}{2 \pi d}$
3 $\frac{7 \mu_{0}}{2 \pi \mathrm{d}}$
4 $\frac{5 \mu_{0}}{2 \pi \mathrm{d}}$
Moving Charges & Magnetism

153226 A bar magnet of magnetic moment $M$ is placed at a distance $D$ with its axis along positive $X$ axis. Likewise, second bar magnet of magnetic moment $M$ is placed at a distance $2 D$ on positive $\mathrm{Y}$-axis and perpendicular to it as shown in the figure. The magnitude of magnetic field at the origin is $|B|=\alpha\left[\frac{\mu_{0}}{4 \pi} \frac{M}{D^{3}}\right]$.
The value of $\alpha$ must be (assume $\mathrm{D}>>l$, where $l$ is the length of magnets)

1 2
2 $\frac{15}{8}$
3 $\frac{17}{8}$
4 $\frac{9}{8}$
Moving Charges & Magnetism

153227 A steady current I flows through a wire with one end at $O$ and the other end extending upto infinity as shown in the figure. The magnetic field at a point $P$, located at a distance $d$ from $O$ is

1 $\frac{\mu_{0} I}{4 \pi d \cos \alpha}(1-\sin \alpha)$
2 $\frac{\mu_{0} I}{2 \pi d \cos \alpha}(1-\sin \alpha)$
3 $\frac{\mu_{0} I}{4 \pi \mathrm{d}}$
4 $\frac{\mu_{0} \mathrm{I}}{4 \pi \mathrm{d} \sin \alpha}(1-\cos \alpha)$
Moving Charges & Magnetism

153228 Consider a current carrying wire shown in the figure. If the radius of the curved part of the wire is $R$ and the linear parts are assumed to be very long, then the magnetic induction of the field at the point $O$ is

1 $\frac{\mu_{0}}{4 \pi} \frac{\mathrm{i}}{\mathrm{R}}(2+\pi)$
2 $\frac{\mu_{0} \mathrm{i}}{2 \pi \mathrm{R}}$
3 $\frac{\mu_{0}}{2} \frac{\mathrm{i}}{\mathrm{R}}$
4 $\frac{\mu_{0}}{4} \frac{\mathrm{i}}{\mathrm{R}}$
Moving Charges & Magnetism

153222 Two short bar magnets each of magnetic moment of $9 \mathrm{Am}^{2}$ are placed such that one is at $x=-3 \mathrm{~cm}$ and the other at $y=-3 \mathrm{~cm}$. If their magnetic moments are directed along positive and negative $X$-directions respectively, then the resultant magnetic field at the origin is

1 $100 \mathrm{~T}$
2 $10 \mathrm{~T}$
3 $0.1 \mathrm{~T}$
4 $0.001 \mathrm{~T}$
Moving Charges & Magnetism

153223 Two infinitely long wires carry currents $4 \mathrm{~A}$ and $3 A$ placed along $X$-axis and $Y$-axis respectively. Magnetic field at a point $P(0,0, d)$ m will be ...... T.

1 $\frac{4 \mu_{0}}{2 \pi d}$
2 $\frac{3 \mu_{0}}{2 \pi d}$
3 $\frac{7 \mu_{0}}{2 \pi \mathrm{d}}$
4 $\frac{5 \mu_{0}}{2 \pi \mathrm{d}}$
Moving Charges & Magnetism

153226 A bar magnet of magnetic moment $M$ is placed at a distance $D$ with its axis along positive $X$ axis. Likewise, second bar magnet of magnetic moment $M$ is placed at a distance $2 D$ on positive $\mathrm{Y}$-axis and perpendicular to it as shown in the figure. The magnitude of magnetic field at the origin is $|B|=\alpha\left[\frac{\mu_{0}}{4 \pi} \frac{M}{D^{3}}\right]$.
The value of $\alpha$ must be (assume $\mathrm{D}>>l$, where $l$ is the length of magnets)

1 2
2 $\frac{15}{8}$
3 $\frac{17}{8}$
4 $\frac{9}{8}$
Moving Charges & Magnetism

153227 A steady current I flows through a wire with one end at $O$ and the other end extending upto infinity as shown in the figure. The magnetic field at a point $P$, located at a distance $d$ from $O$ is

1 $\frac{\mu_{0} I}{4 \pi d \cos \alpha}(1-\sin \alpha)$
2 $\frac{\mu_{0} I}{2 \pi d \cos \alpha}(1-\sin \alpha)$
3 $\frac{\mu_{0} I}{4 \pi \mathrm{d}}$
4 $\frac{\mu_{0} \mathrm{I}}{4 \pi \mathrm{d} \sin \alpha}(1-\cos \alpha)$
Moving Charges & Magnetism

153228 Consider a current carrying wire shown in the figure. If the radius of the curved part of the wire is $R$ and the linear parts are assumed to be very long, then the magnetic induction of the field at the point $O$ is

1 $\frac{\mu_{0}}{4 \pi} \frac{\mathrm{i}}{\mathrm{R}}(2+\pi)$
2 $\frac{\mu_{0} \mathrm{i}}{2 \pi \mathrm{R}}$
3 $\frac{\mu_{0}}{2} \frac{\mathrm{i}}{\mathrm{R}}$
4 $\frac{\mu_{0}}{4} \frac{\mathrm{i}}{\mathrm{R}}$