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

153263 A horizontal overhead powerline is at height of $4 \mathrm{~m}$ from the ground and carries a current of $100 \mathrm{~A}$ from east to west. The magnetic field directly below it on the ground is $\left(\mu_{0}=4 \pi \times 10^{-}\right.$ ${ }^{7} \mathbf{T m ~ A ^ { - 1 } )}$

1 $2.5 \times 10^{-7} \mathrm{~T}$ southward
2 $5 \times 10^{-6} \mathrm{~T}$ northward
3 $5 \times 10^{-6} \mathrm{~T}$ southward
4 $2.5 \times 10^{-7} \mathrm{~T}$ northward
Moving Charges & Magnetism

153264 A wire carrying current $I$ has the shape as shown in adjoining figure. Linear parts of the wire are very long and parallel to $X$-axis while semicircular portion of radius $\mathrm{R}$ is lying in $\mathrm{Y}-\mathrm{Z}$ plane. Magnetic field at point $O$ is :

1 $\overrightarrow{\mathrm{B}}=-\frac{\mu_{0}}{4 \pi} \frac{\mathrm{I}}{\mathrm{R}}(\mu \hat{\mathrm{i}} \times 2 \hat{\mathrm{k}})$
2 $\vec{B}=-\frac{\mu_{0}}{4 \pi} \frac{I}{R}(\pi \hat{i}+2 \hat{k})$
3 $\overrightarrow{\mathrm{B}}=-\frac{\mu_{0}}{4 \pi} \frac{\mathrm{I}}{\mathrm{R}}(\pi \hat{\mathrm{i}}-2 \hat{\mathrm{k}})$
4 $\overrightarrow{\mathrm{B}}=-\frac{\mu_{0}}{4 \pi} \frac{\mathrm{I}}{\mathrm{R}}(\pi \hat{\mathrm{i}}+2 \hat{\mathrm{k}})$
Moving Charges & Magnetism

153265 Four very long current carrying wires in the same plane intersect to form a square $40.0 \mathrm{~cm}$ on each side as shown in the figure. What is the magnitude of current $I$ so that the magnetic field at the centre of the square is zero?

1 $22 \mathrm{~A}$
2 $38 \mathrm{~A}$
3 $2 \mathrm{~A}$
4 $18 \mathrm{~A}$
Moving Charges & Magnetism

153266 A conducting loop carrying a current $I$ is placed in a uniform magnetic field pointing into the plane of the paper as shown. The loop will have a tendency to

1 expand
2 move towards +ve $\mathrm{x}$-axis
3 contract
4 move towards -ve x-axis
Moving Charges & Magnetism

153268 A particle having charge 10 times that of the electron revolves in a circular path of radius $0.4 \mathrm{~m}$ with an angular speed of one rotation per second. The magnetic induction produced at the centre of the circular path is

1 $4 \pi \times 10^{-26} \mathrm{~T}$
2 $2 \pi \times 10^{-26} \mathrm{~T}$
3 $16 \pi \times 10^{-26} \mathrm{~T}$
4 $8 \pi \times 10^{-25} \mathrm{~T}$
5 $9 \pi \times 10^{-25} \mathrm{~T}$
Moving Charges & Magnetism

153263 A horizontal overhead powerline is at height of $4 \mathrm{~m}$ from the ground and carries a current of $100 \mathrm{~A}$ from east to west. The magnetic field directly below it on the ground is $\left(\mu_{0}=4 \pi \times 10^{-}\right.$ ${ }^{7} \mathbf{T m ~ A ^ { - 1 } )}$

1 $2.5 \times 10^{-7} \mathrm{~T}$ southward
2 $5 \times 10^{-6} \mathrm{~T}$ northward
3 $5 \times 10^{-6} \mathrm{~T}$ southward
4 $2.5 \times 10^{-7} \mathrm{~T}$ northward
Moving Charges & Magnetism

153264 A wire carrying current $I$ has the shape as shown in adjoining figure. Linear parts of the wire are very long and parallel to $X$-axis while semicircular portion of radius $\mathrm{R}$ is lying in $\mathrm{Y}-\mathrm{Z}$ plane. Magnetic field at point $O$ is :

1 $\overrightarrow{\mathrm{B}}=-\frac{\mu_{0}}{4 \pi} \frac{\mathrm{I}}{\mathrm{R}}(\mu \hat{\mathrm{i}} \times 2 \hat{\mathrm{k}})$
2 $\vec{B}=-\frac{\mu_{0}}{4 \pi} \frac{I}{R}(\pi \hat{i}+2 \hat{k})$
3 $\overrightarrow{\mathrm{B}}=-\frac{\mu_{0}}{4 \pi} \frac{\mathrm{I}}{\mathrm{R}}(\pi \hat{\mathrm{i}}-2 \hat{\mathrm{k}})$
4 $\overrightarrow{\mathrm{B}}=-\frac{\mu_{0}}{4 \pi} \frac{\mathrm{I}}{\mathrm{R}}(\pi \hat{\mathrm{i}}+2 \hat{\mathrm{k}})$
Moving Charges & Magnetism

153265 Four very long current carrying wires in the same plane intersect to form a square $40.0 \mathrm{~cm}$ on each side as shown in the figure. What is the magnitude of current $I$ so that the magnetic field at the centre of the square is zero?

1 $22 \mathrm{~A}$
2 $38 \mathrm{~A}$
3 $2 \mathrm{~A}$
4 $18 \mathrm{~A}$
Moving Charges & Magnetism

153266 A conducting loop carrying a current $I$ is placed in a uniform magnetic field pointing into the plane of the paper as shown. The loop will have a tendency to

1 expand
2 move towards +ve $\mathrm{x}$-axis
3 contract
4 move towards -ve x-axis
Moving Charges & Magnetism

153268 A particle having charge 10 times that of the electron revolves in a circular path of radius $0.4 \mathrm{~m}$ with an angular speed of one rotation per second. The magnetic induction produced at the centre of the circular path is

1 $4 \pi \times 10^{-26} \mathrm{~T}$
2 $2 \pi \times 10^{-26} \mathrm{~T}$
3 $16 \pi \times 10^{-26} \mathrm{~T}$
4 $8 \pi \times 10^{-25} \mathrm{~T}$
5 $9 \pi \times 10^{-25} \mathrm{~T}$
Moving Charges & Magnetism

153263 A horizontal overhead powerline is at height of $4 \mathrm{~m}$ from the ground and carries a current of $100 \mathrm{~A}$ from east to west. The magnetic field directly below it on the ground is $\left(\mu_{0}=4 \pi \times 10^{-}\right.$ ${ }^{7} \mathbf{T m ~ A ^ { - 1 } )}$

1 $2.5 \times 10^{-7} \mathrm{~T}$ southward
2 $5 \times 10^{-6} \mathrm{~T}$ northward
3 $5 \times 10^{-6} \mathrm{~T}$ southward
4 $2.5 \times 10^{-7} \mathrm{~T}$ northward
Moving Charges & Magnetism

153264 A wire carrying current $I$ has the shape as shown in adjoining figure. Linear parts of the wire are very long and parallel to $X$-axis while semicircular portion of radius $\mathrm{R}$ is lying in $\mathrm{Y}-\mathrm{Z}$ plane. Magnetic field at point $O$ is :

1 $\overrightarrow{\mathrm{B}}=-\frac{\mu_{0}}{4 \pi} \frac{\mathrm{I}}{\mathrm{R}}(\mu \hat{\mathrm{i}} \times 2 \hat{\mathrm{k}})$
2 $\vec{B}=-\frac{\mu_{0}}{4 \pi} \frac{I}{R}(\pi \hat{i}+2 \hat{k})$
3 $\overrightarrow{\mathrm{B}}=-\frac{\mu_{0}}{4 \pi} \frac{\mathrm{I}}{\mathrm{R}}(\pi \hat{\mathrm{i}}-2 \hat{\mathrm{k}})$
4 $\overrightarrow{\mathrm{B}}=-\frac{\mu_{0}}{4 \pi} \frac{\mathrm{I}}{\mathrm{R}}(\pi \hat{\mathrm{i}}+2 \hat{\mathrm{k}})$
Moving Charges & Magnetism

153265 Four very long current carrying wires in the same plane intersect to form a square $40.0 \mathrm{~cm}$ on each side as shown in the figure. What is the magnitude of current $I$ so that the magnetic field at the centre of the square is zero?

1 $22 \mathrm{~A}$
2 $38 \mathrm{~A}$
3 $2 \mathrm{~A}$
4 $18 \mathrm{~A}$
Moving Charges & Magnetism

153266 A conducting loop carrying a current $I$ is placed in a uniform magnetic field pointing into the plane of the paper as shown. The loop will have a tendency to

1 expand
2 move towards +ve $\mathrm{x}$-axis
3 contract
4 move towards -ve x-axis
Moving Charges & Magnetism

153268 A particle having charge 10 times that of the electron revolves in a circular path of radius $0.4 \mathrm{~m}$ with an angular speed of one rotation per second. The magnetic induction produced at the centre of the circular path is

1 $4 \pi \times 10^{-26} \mathrm{~T}$
2 $2 \pi \times 10^{-26} \mathrm{~T}$
3 $16 \pi \times 10^{-26} \mathrm{~T}$
4 $8 \pi \times 10^{-25} \mathrm{~T}$
5 $9 \pi \times 10^{-25} \mathrm{~T}$
Moving Charges & Magnetism

153263 A horizontal overhead powerline is at height of $4 \mathrm{~m}$ from the ground and carries a current of $100 \mathrm{~A}$ from east to west. The magnetic field directly below it on the ground is $\left(\mu_{0}=4 \pi \times 10^{-}\right.$ ${ }^{7} \mathbf{T m ~ A ^ { - 1 } )}$

1 $2.5 \times 10^{-7} \mathrm{~T}$ southward
2 $5 \times 10^{-6} \mathrm{~T}$ northward
3 $5 \times 10^{-6} \mathrm{~T}$ southward
4 $2.5 \times 10^{-7} \mathrm{~T}$ northward
Moving Charges & Magnetism

153264 A wire carrying current $I$ has the shape as shown in adjoining figure. Linear parts of the wire are very long and parallel to $X$-axis while semicircular portion of radius $\mathrm{R}$ is lying in $\mathrm{Y}-\mathrm{Z}$ plane. Magnetic field at point $O$ is :

1 $\overrightarrow{\mathrm{B}}=-\frac{\mu_{0}}{4 \pi} \frac{\mathrm{I}}{\mathrm{R}}(\mu \hat{\mathrm{i}} \times 2 \hat{\mathrm{k}})$
2 $\vec{B}=-\frac{\mu_{0}}{4 \pi} \frac{I}{R}(\pi \hat{i}+2 \hat{k})$
3 $\overrightarrow{\mathrm{B}}=-\frac{\mu_{0}}{4 \pi} \frac{\mathrm{I}}{\mathrm{R}}(\pi \hat{\mathrm{i}}-2 \hat{\mathrm{k}})$
4 $\overrightarrow{\mathrm{B}}=-\frac{\mu_{0}}{4 \pi} \frac{\mathrm{I}}{\mathrm{R}}(\pi \hat{\mathrm{i}}+2 \hat{\mathrm{k}})$
Moving Charges & Magnetism

153265 Four very long current carrying wires in the same plane intersect to form a square $40.0 \mathrm{~cm}$ on each side as shown in the figure. What is the magnitude of current $I$ so that the magnetic field at the centre of the square is zero?

1 $22 \mathrm{~A}$
2 $38 \mathrm{~A}$
3 $2 \mathrm{~A}$
4 $18 \mathrm{~A}$
Moving Charges & Magnetism

153266 A conducting loop carrying a current $I$ is placed in a uniform magnetic field pointing into the plane of the paper as shown. The loop will have a tendency to

1 expand
2 move towards +ve $\mathrm{x}$-axis
3 contract
4 move towards -ve x-axis
Moving Charges & Magnetism

153268 A particle having charge 10 times that of the electron revolves in a circular path of radius $0.4 \mathrm{~m}$ with an angular speed of one rotation per second. The magnetic induction produced at the centre of the circular path is

1 $4 \pi \times 10^{-26} \mathrm{~T}$
2 $2 \pi \times 10^{-26} \mathrm{~T}$
3 $16 \pi \times 10^{-26} \mathrm{~T}$
4 $8 \pi \times 10^{-25} \mathrm{~T}$
5 $9 \pi \times 10^{-25} \mathrm{~T}$
Moving Charges & Magnetism

153263 A horizontal overhead powerline is at height of $4 \mathrm{~m}$ from the ground and carries a current of $100 \mathrm{~A}$ from east to west. The magnetic field directly below it on the ground is $\left(\mu_{0}=4 \pi \times 10^{-}\right.$ ${ }^{7} \mathbf{T m ~ A ^ { - 1 } )}$

1 $2.5 \times 10^{-7} \mathrm{~T}$ southward
2 $5 \times 10^{-6} \mathrm{~T}$ northward
3 $5 \times 10^{-6} \mathrm{~T}$ southward
4 $2.5 \times 10^{-7} \mathrm{~T}$ northward
Moving Charges & Magnetism

153264 A wire carrying current $I$ has the shape as shown in adjoining figure. Linear parts of the wire are very long and parallel to $X$-axis while semicircular portion of radius $\mathrm{R}$ is lying in $\mathrm{Y}-\mathrm{Z}$ plane. Magnetic field at point $O$ is :

1 $\overrightarrow{\mathrm{B}}=-\frac{\mu_{0}}{4 \pi} \frac{\mathrm{I}}{\mathrm{R}}(\mu \hat{\mathrm{i}} \times 2 \hat{\mathrm{k}})$
2 $\vec{B}=-\frac{\mu_{0}}{4 \pi} \frac{I}{R}(\pi \hat{i}+2 \hat{k})$
3 $\overrightarrow{\mathrm{B}}=-\frac{\mu_{0}}{4 \pi} \frac{\mathrm{I}}{\mathrm{R}}(\pi \hat{\mathrm{i}}-2 \hat{\mathrm{k}})$
4 $\overrightarrow{\mathrm{B}}=-\frac{\mu_{0}}{4 \pi} \frac{\mathrm{I}}{\mathrm{R}}(\pi \hat{\mathrm{i}}+2 \hat{\mathrm{k}})$
Moving Charges & Magnetism

153265 Four very long current carrying wires in the same plane intersect to form a square $40.0 \mathrm{~cm}$ on each side as shown in the figure. What is the magnitude of current $I$ so that the magnetic field at the centre of the square is zero?

1 $22 \mathrm{~A}$
2 $38 \mathrm{~A}$
3 $2 \mathrm{~A}$
4 $18 \mathrm{~A}$
Moving Charges & Magnetism

153266 A conducting loop carrying a current $I$ is placed in a uniform magnetic field pointing into the plane of the paper as shown. The loop will have a tendency to

1 expand
2 move towards +ve $\mathrm{x}$-axis
3 contract
4 move towards -ve x-axis
Moving Charges & Magnetism

153268 A particle having charge 10 times that of the electron revolves in a circular path of radius $0.4 \mathrm{~m}$ with an angular speed of one rotation per second. The magnetic induction produced at the centre of the circular path is

1 $4 \pi \times 10^{-26} \mathrm{~T}$
2 $2 \pi \times 10^{-26} \mathrm{~T}$
3 $16 \pi \times 10^{-26} \mathrm{~T}$
4 $8 \pi \times 10^{-25} \mathrm{~T}$
5 $9 \pi \times 10^{-25} \mathrm{~T}$