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

153298 Two long wires each parallel to the z-axis and each carrying current $I$, are at $(0,0,0)$ and $(a$, $b, 0)$. What is the force per unit length of each wire?

1 $\frac{\mu_{0} I^{2}}{2 \pi\left(a^{2}+b^{2}\right)}$
2 $\frac{\mu_{0} \mathrm{I}^{2}}{2 \pi\left(\mathrm{a}^{2}+\mathrm{b}^{2}\right)^{\frac{3}{2}}}$
3 $\frac{\mu_{0} I^{2}(a+b)}{2 \pi\left(a^{2}+b^{2}\right)}$
4 None of the above
Moving Charges & Magnetism

153300 Two concentric coils each of radius equal to $2 \pi$ $\mathrm{cm}$ are placed at right angles to each other. If $3 \mathrm{~A}$ and $4 \mathrm{~A}$ are the currents flowing through the two coils respectively. The magnetic induction (in $\mathrm{Wb} \mathrm{m}^{-2}$ ) at the centre of the coils will be:

1 $5 \times 10^{-5}$
2 $12 \times 10^{-5}$
3 $7 \times 10^{-5}$
4 $10^{-5}$
Moving Charges & Magnetism

153301 In the loop shown, the magnetic induction at the point $O$ is:

1 zero
2 $\frac{\mu_{0} I}{8}\left(\frac{R_{1}-R_{2}}{R_{1} R_{2}}\right)$
3 $\frac{\mu_{0} I}{8}\left(\frac{R_{1}+R_{2}}{R_{1} R_{2}}\right)$
4 $\frac{\mu_{0} I}{8}\left(\frac{R_{1} R_{2}}{R_{1}+R_{2}}\right)$
Moving Charges & Magnetism

153303 Magnetic field at the centre of a circular coil of radius $R$ due to current $i$ flowing through it is $B$. The magnetic field at a point along the axis at distance $R$ from the centre is:

1 $\frac{\mathrm{B}}{2}$
2 $\frac{B}{4}$
3 $\frac{\mathrm{B}}{\sqrt{8}}$
4 $\sqrt{8} \mathrm{~B}$
Moving Charges & Magnetism

153304 A wire $P Q R$ is bent as shown in figure and is placed in a region of uniform magnetic field $B$. The length of $P Q=Q R=l$. A current $I$ ampere flows through the wire as shown. The magnitude of the force on $P Q$ and $Q R$ will be:

1 $\mathrm{BI} l, 0$
2 $2 \mathrm{BI} l, 0$
3 $0, \mathrm{BI} l$
4 0,0
Moving Charges & Magnetism

153298 Two long wires each parallel to the z-axis and each carrying current $I$, are at $(0,0,0)$ and $(a$, $b, 0)$. What is the force per unit length of each wire?

1 $\frac{\mu_{0} I^{2}}{2 \pi\left(a^{2}+b^{2}\right)}$
2 $\frac{\mu_{0} \mathrm{I}^{2}}{2 \pi\left(\mathrm{a}^{2}+\mathrm{b}^{2}\right)^{\frac{3}{2}}}$
3 $\frac{\mu_{0} I^{2}(a+b)}{2 \pi\left(a^{2}+b^{2}\right)}$
4 None of the above
Moving Charges & Magnetism

153300 Two concentric coils each of radius equal to $2 \pi$ $\mathrm{cm}$ are placed at right angles to each other. If $3 \mathrm{~A}$ and $4 \mathrm{~A}$ are the currents flowing through the two coils respectively. The magnetic induction (in $\mathrm{Wb} \mathrm{m}^{-2}$ ) at the centre of the coils will be:

1 $5 \times 10^{-5}$
2 $12 \times 10^{-5}$
3 $7 \times 10^{-5}$
4 $10^{-5}$
Moving Charges & Magnetism

153301 In the loop shown, the magnetic induction at the point $O$ is:

1 zero
2 $\frac{\mu_{0} I}{8}\left(\frac{R_{1}-R_{2}}{R_{1} R_{2}}\right)$
3 $\frac{\mu_{0} I}{8}\left(\frac{R_{1}+R_{2}}{R_{1} R_{2}}\right)$
4 $\frac{\mu_{0} I}{8}\left(\frac{R_{1} R_{2}}{R_{1}+R_{2}}\right)$
Moving Charges & Magnetism

153303 Magnetic field at the centre of a circular coil of radius $R$ due to current $i$ flowing through it is $B$. The magnetic field at a point along the axis at distance $R$ from the centre is:

1 $\frac{\mathrm{B}}{2}$
2 $\frac{B}{4}$
3 $\frac{\mathrm{B}}{\sqrt{8}}$
4 $\sqrt{8} \mathrm{~B}$
Moving Charges & Magnetism

153304 A wire $P Q R$ is bent as shown in figure and is placed in a region of uniform magnetic field $B$. The length of $P Q=Q R=l$. A current $I$ ampere flows through the wire as shown. The magnitude of the force on $P Q$ and $Q R$ will be:

1 $\mathrm{BI} l, 0$
2 $2 \mathrm{BI} l, 0$
3 $0, \mathrm{BI} l$
4 0,0
Moving Charges & Magnetism

153298 Two long wires each parallel to the z-axis and each carrying current $I$, are at $(0,0,0)$ and $(a$, $b, 0)$. What is the force per unit length of each wire?

1 $\frac{\mu_{0} I^{2}}{2 \pi\left(a^{2}+b^{2}\right)}$
2 $\frac{\mu_{0} \mathrm{I}^{2}}{2 \pi\left(\mathrm{a}^{2}+\mathrm{b}^{2}\right)^{\frac{3}{2}}}$
3 $\frac{\mu_{0} I^{2}(a+b)}{2 \pi\left(a^{2}+b^{2}\right)}$
4 None of the above
Moving Charges & Magnetism

153300 Two concentric coils each of radius equal to $2 \pi$ $\mathrm{cm}$ are placed at right angles to each other. If $3 \mathrm{~A}$ and $4 \mathrm{~A}$ are the currents flowing through the two coils respectively. The magnetic induction (in $\mathrm{Wb} \mathrm{m}^{-2}$ ) at the centre of the coils will be:

1 $5 \times 10^{-5}$
2 $12 \times 10^{-5}$
3 $7 \times 10^{-5}$
4 $10^{-5}$
Moving Charges & Magnetism

153301 In the loop shown, the magnetic induction at the point $O$ is:

1 zero
2 $\frac{\mu_{0} I}{8}\left(\frac{R_{1}-R_{2}}{R_{1} R_{2}}\right)$
3 $\frac{\mu_{0} I}{8}\left(\frac{R_{1}+R_{2}}{R_{1} R_{2}}\right)$
4 $\frac{\mu_{0} I}{8}\left(\frac{R_{1} R_{2}}{R_{1}+R_{2}}\right)$
Moving Charges & Magnetism

153303 Magnetic field at the centre of a circular coil of radius $R$ due to current $i$ flowing through it is $B$. The magnetic field at a point along the axis at distance $R$ from the centre is:

1 $\frac{\mathrm{B}}{2}$
2 $\frac{B}{4}$
3 $\frac{\mathrm{B}}{\sqrt{8}}$
4 $\sqrt{8} \mathrm{~B}$
Moving Charges & Magnetism

153304 A wire $P Q R$ is bent as shown in figure and is placed in a region of uniform magnetic field $B$. The length of $P Q=Q R=l$. A current $I$ ampere flows through the wire as shown. The magnitude of the force on $P Q$ and $Q R$ will be:

1 $\mathrm{BI} l, 0$
2 $2 \mathrm{BI} l, 0$
3 $0, \mathrm{BI} l$
4 0,0
Moving Charges & Magnetism

153298 Two long wires each parallel to the z-axis and each carrying current $I$, are at $(0,0,0)$ and $(a$, $b, 0)$. What is the force per unit length of each wire?

1 $\frac{\mu_{0} I^{2}}{2 \pi\left(a^{2}+b^{2}\right)}$
2 $\frac{\mu_{0} \mathrm{I}^{2}}{2 \pi\left(\mathrm{a}^{2}+\mathrm{b}^{2}\right)^{\frac{3}{2}}}$
3 $\frac{\mu_{0} I^{2}(a+b)}{2 \pi\left(a^{2}+b^{2}\right)}$
4 None of the above
Moving Charges & Magnetism

153300 Two concentric coils each of radius equal to $2 \pi$ $\mathrm{cm}$ are placed at right angles to each other. If $3 \mathrm{~A}$ and $4 \mathrm{~A}$ are the currents flowing through the two coils respectively. The magnetic induction (in $\mathrm{Wb} \mathrm{m}^{-2}$ ) at the centre of the coils will be:

1 $5 \times 10^{-5}$
2 $12 \times 10^{-5}$
3 $7 \times 10^{-5}$
4 $10^{-5}$
Moving Charges & Magnetism

153301 In the loop shown, the magnetic induction at the point $O$ is:

1 zero
2 $\frac{\mu_{0} I}{8}\left(\frac{R_{1}-R_{2}}{R_{1} R_{2}}\right)$
3 $\frac{\mu_{0} I}{8}\left(\frac{R_{1}+R_{2}}{R_{1} R_{2}}\right)$
4 $\frac{\mu_{0} I}{8}\left(\frac{R_{1} R_{2}}{R_{1}+R_{2}}\right)$
Moving Charges & Magnetism

153303 Magnetic field at the centre of a circular coil of radius $R$ due to current $i$ flowing through it is $B$. The magnetic field at a point along the axis at distance $R$ from the centre is:

1 $\frac{\mathrm{B}}{2}$
2 $\frac{B}{4}$
3 $\frac{\mathrm{B}}{\sqrt{8}}$
4 $\sqrt{8} \mathrm{~B}$
Moving Charges & Magnetism

153304 A wire $P Q R$ is bent as shown in figure and is placed in a region of uniform magnetic field $B$. The length of $P Q=Q R=l$. A current $I$ ampere flows through the wire as shown. The magnitude of the force on $P Q$ and $Q R$ will be:

1 $\mathrm{BI} l, 0$
2 $2 \mathrm{BI} l, 0$
3 $0, \mathrm{BI} l$
4 0,0
Moving Charges & Magnetism

153298 Two long wires each parallel to the z-axis and each carrying current $I$, are at $(0,0,0)$ and $(a$, $b, 0)$. What is the force per unit length of each wire?

1 $\frac{\mu_{0} I^{2}}{2 \pi\left(a^{2}+b^{2}\right)}$
2 $\frac{\mu_{0} \mathrm{I}^{2}}{2 \pi\left(\mathrm{a}^{2}+\mathrm{b}^{2}\right)^{\frac{3}{2}}}$
3 $\frac{\mu_{0} I^{2}(a+b)}{2 \pi\left(a^{2}+b^{2}\right)}$
4 None of the above
Moving Charges & Magnetism

153300 Two concentric coils each of radius equal to $2 \pi$ $\mathrm{cm}$ are placed at right angles to each other. If $3 \mathrm{~A}$ and $4 \mathrm{~A}$ are the currents flowing through the two coils respectively. The magnetic induction (in $\mathrm{Wb} \mathrm{m}^{-2}$ ) at the centre of the coils will be:

1 $5 \times 10^{-5}$
2 $12 \times 10^{-5}$
3 $7 \times 10^{-5}$
4 $10^{-5}$
Moving Charges & Magnetism

153301 In the loop shown, the magnetic induction at the point $O$ is:

1 zero
2 $\frac{\mu_{0} I}{8}\left(\frac{R_{1}-R_{2}}{R_{1} R_{2}}\right)$
3 $\frac{\mu_{0} I}{8}\left(\frac{R_{1}+R_{2}}{R_{1} R_{2}}\right)$
4 $\frac{\mu_{0} I}{8}\left(\frac{R_{1} R_{2}}{R_{1}+R_{2}}\right)$
Moving Charges & Magnetism

153303 Magnetic field at the centre of a circular coil of radius $R$ due to current $i$ flowing through it is $B$. The magnetic field at a point along the axis at distance $R$ from the centre is:

1 $\frac{\mathrm{B}}{2}$
2 $\frac{B}{4}$
3 $\frac{\mathrm{B}}{\sqrt{8}}$
4 $\sqrt{8} \mathrm{~B}$
Moving Charges & Magnetism

153304 A wire $P Q R$ is bent as shown in figure and is placed in a region of uniform magnetic field $B$. The length of $P Q=Q R=l$. A current $I$ ampere flows through the wire as shown. The magnitude of the force on $P Q$ and $Q R$ will be:

1 $\mathrm{BI} l, 0$
2 $2 \mathrm{BI} l, 0$
3 $0, \mathrm{BI} l$
4 0,0