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

153349 Under the influence of a uniform magnetic field a charged particle is moving in a circle of radius $R$ with constant speed $v$. The time period of the motion

1 depends on $\mathrm{v}$ and not on $\mathrm{R}$
2 depends on both $\mathrm{R}$ and $\mathrm{v}$
3 is independent of both $\mathrm{R}$ and $\mathrm{v}$
4 depends on $\mathrm{R}$ and not on $\mathrm{V}$
Moving Charges & Magnetism

153350 When a charged particle moving with velocity $v$ is subjected to a magnetic field of induction $B$, the force on it is non-zero. This implies that

1 angle between $v$ and B is necessarily $90^{\circ}$
2 angle between $\mathrm{v}$ and $\mathrm{B}$ can have any value other than $90^{\circ}$
3 angle between $\mathrm{v}$ and $\mathrm{B}$ can have any value other than zero and $180^{\circ}$
4 angle between $\mathrm{v}$ and $\mathrm{B}$ is either zero or $180^{\circ}$
Moving Charges & Magnetism

153352 An electron is moving in a circular path under the influence of a transverse magnetic field of $3.57 \times 10^{-2} \mathrm{~T}$. If the value of $\mathrm{e} / \mathrm{m}$ is $1.76 \times 10^{11}$ $\mathrm{C} / \mathrm{kg}$, the frequency of revolution of the electron is

1 $1 \mathrm{GHz}$
2 $100 \mathrm{MHz}$
3 $62.8 \mathrm{MHz}$
4 $6.28 \mathrm{MHz}$
Moving Charges & Magnetism

153353 An alternating electric field of frequency $v$, is applied across the dees (radius $=R$ ) of a cyclotron that is being used to accelerate protons $($ mass $=m)$. The operating magnetic field (B) used in the cyclotron and the kinetic energy $(K)$ of proton beam, produced by it, are given by

1 $\mathrm{B}=\frac{\mathrm{mv}}{\mathrm{e}}$ and $\mathrm{K}=2 \mathrm{~m} \pi^{2} \mathrm{v}^{2} \mathrm{R}^{2}$
2 $\mathrm{B}=\frac{2 \pi \mathrm{mv}}{\mathrm{e}}$ and $\mathrm{K}=\mathrm{m}^{2} \pi \mathrm{vR} \mathrm{R}^{2}$
3 $\mathrm{B}=\frac{2 \pi \mathrm{mv}}{\mathrm{e}}$ and $\mathrm{K}=2 \mathrm{~m} \pi^{2} \mathrm{v}^{2} \mathrm{R}^{2}$
4 $\mathrm{B}=\frac{\mathrm{mv}}{\mathrm{e}}$ and $\mathrm{K}=\mathrm{m}^{2} \pi \mathrm{vR}^{2}$
Moving Charges & Magnetism

153349 Under the influence of a uniform magnetic field a charged particle is moving in a circle of radius $R$ with constant speed $v$. The time period of the motion

1 depends on $\mathrm{v}$ and not on $\mathrm{R}$
2 depends on both $\mathrm{R}$ and $\mathrm{v}$
3 is independent of both $\mathrm{R}$ and $\mathrm{v}$
4 depends on $\mathrm{R}$ and not on $\mathrm{V}$
Moving Charges & Magnetism

153350 When a charged particle moving with velocity $v$ is subjected to a magnetic field of induction $B$, the force on it is non-zero. This implies that

1 angle between $v$ and B is necessarily $90^{\circ}$
2 angle between $\mathrm{v}$ and $\mathrm{B}$ can have any value other than $90^{\circ}$
3 angle between $\mathrm{v}$ and $\mathrm{B}$ can have any value other than zero and $180^{\circ}$
4 angle between $\mathrm{v}$ and $\mathrm{B}$ is either zero or $180^{\circ}$
Moving Charges & Magnetism

153352 An electron is moving in a circular path under the influence of a transverse magnetic field of $3.57 \times 10^{-2} \mathrm{~T}$. If the value of $\mathrm{e} / \mathrm{m}$ is $1.76 \times 10^{11}$ $\mathrm{C} / \mathrm{kg}$, the frequency of revolution of the electron is

1 $1 \mathrm{GHz}$
2 $100 \mathrm{MHz}$
3 $62.8 \mathrm{MHz}$
4 $6.28 \mathrm{MHz}$
Moving Charges & Magnetism

153353 An alternating electric field of frequency $v$, is applied across the dees (radius $=R$ ) of a cyclotron that is being used to accelerate protons $($ mass $=m)$. The operating magnetic field (B) used in the cyclotron and the kinetic energy $(K)$ of proton beam, produced by it, are given by

1 $\mathrm{B}=\frac{\mathrm{mv}}{\mathrm{e}}$ and $\mathrm{K}=2 \mathrm{~m} \pi^{2} \mathrm{v}^{2} \mathrm{R}^{2}$
2 $\mathrm{B}=\frac{2 \pi \mathrm{mv}}{\mathrm{e}}$ and $\mathrm{K}=\mathrm{m}^{2} \pi \mathrm{vR} \mathrm{R}^{2}$
3 $\mathrm{B}=\frac{2 \pi \mathrm{mv}}{\mathrm{e}}$ and $\mathrm{K}=2 \mathrm{~m} \pi^{2} \mathrm{v}^{2} \mathrm{R}^{2}$
4 $\mathrm{B}=\frac{\mathrm{mv}}{\mathrm{e}}$ and $\mathrm{K}=\mathrm{m}^{2} \pi \mathrm{vR}^{2}$
Moving Charges & Magnetism

153349 Under the influence of a uniform magnetic field a charged particle is moving in a circle of radius $R$ with constant speed $v$. The time period of the motion

1 depends on $\mathrm{v}$ and not on $\mathrm{R}$
2 depends on both $\mathrm{R}$ and $\mathrm{v}$
3 is independent of both $\mathrm{R}$ and $\mathrm{v}$
4 depends on $\mathrm{R}$ and not on $\mathrm{V}$
Moving Charges & Magnetism

153350 When a charged particle moving with velocity $v$ is subjected to a magnetic field of induction $B$, the force on it is non-zero. This implies that

1 angle between $v$ and B is necessarily $90^{\circ}$
2 angle between $\mathrm{v}$ and $\mathrm{B}$ can have any value other than $90^{\circ}$
3 angle between $\mathrm{v}$ and $\mathrm{B}$ can have any value other than zero and $180^{\circ}$
4 angle between $\mathrm{v}$ and $\mathrm{B}$ is either zero or $180^{\circ}$
Moving Charges & Magnetism

153352 An electron is moving in a circular path under the influence of a transverse magnetic field of $3.57 \times 10^{-2} \mathrm{~T}$. If the value of $\mathrm{e} / \mathrm{m}$ is $1.76 \times 10^{11}$ $\mathrm{C} / \mathrm{kg}$, the frequency of revolution of the electron is

1 $1 \mathrm{GHz}$
2 $100 \mathrm{MHz}$
3 $62.8 \mathrm{MHz}$
4 $6.28 \mathrm{MHz}$
Moving Charges & Magnetism

153353 An alternating electric field of frequency $v$, is applied across the dees (radius $=R$ ) of a cyclotron that is being used to accelerate protons $($ mass $=m)$. The operating magnetic field (B) used in the cyclotron and the kinetic energy $(K)$ of proton beam, produced by it, are given by

1 $\mathrm{B}=\frac{\mathrm{mv}}{\mathrm{e}}$ and $\mathrm{K}=2 \mathrm{~m} \pi^{2} \mathrm{v}^{2} \mathrm{R}^{2}$
2 $\mathrm{B}=\frac{2 \pi \mathrm{mv}}{\mathrm{e}}$ and $\mathrm{K}=\mathrm{m}^{2} \pi \mathrm{vR} \mathrm{R}^{2}$
3 $\mathrm{B}=\frac{2 \pi \mathrm{mv}}{\mathrm{e}}$ and $\mathrm{K}=2 \mathrm{~m} \pi^{2} \mathrm{v}^{2} \mathrm{R}^{2}$
4 $\mathrm{B}=\frac{\mathrm{mv}}{\mathrm{e}}$ and $\mathrm{K}=\mathrm{m}^{2} \pi \mathrm{vR}^{2}$
Moving Charges & Magnetism

153349 Under the influence of a uniform magnetic field a charged particle is moving in a circle of radius $R$ with constant speed $v$. The time period of the motion

1 depends on $\mathrm{v}$ and not on $\mathrm{R}$
2 depends on both $\mathrm{R}$ and $\mathrm{v}$
3 is independent of both $\mathrm{R}$ and $\mathrm{v}$
4 depends on $\mathrm{R}$ and not on $\mathrm{V}$
Moving Charges & Magnetism

153350 When a charged particle moving with velocity $v$ is subjected to a magnetic field of induction $B$, the force on it is non-zero. This implies that

1 angle between $v$ and B is necessarily $90^{\circ}$
2 angle between $\mathrm{v}$ and $\mathrm{B}$ can have any value other than $90^{\circ}$
3 angle between $\mathrm{v}$ and $\mathrm{B}$ can have any value other than zero and $180^{\circ}$
4 angle between $\mathrm{v}$ and $\mathrm{B}$ is either zero or $180^{\circ}$
Moving Charges & Magnetism

153352 An electron is moving in a circular path under the influence of a transverse magnetic field of $3.57 \times 10^{-2} \mathrm{~T}$. If the value of $\mathrm{e} / \mathrm{m}$ is $1.76 \times 10^{11}$ $\mathrm{C} / \mathrm{kg}$, the frequency of revolution of the electron is

1 $1 \mathrm{GHz}$
2 $100 \mathrm{MHz}$
3 $62.8 \mathrm{MHz}$
4 $6.28 \mathrm{MHz}$
Moving Charges & Magnetism

153353 An alternating electric field of frequency $v$, is applied across the dees (radius $=R$ ) of a cyclotron that is being used to accelerate protons $($ mass $=m)$. The operating magnetic field (B) used in the cyclotron and the kinetic energy $(K)$ of proton beam, produced by it, are given by

1 $\mathrm{B}=\frac{\mathrm{mv}}{\mathrm{e}}$ and $\mathrm{K}=2 \mathrm{~m} \pi^{2} \mathrm{v}^{2} \mathrm{R}^{2}$
2 $\mathrm{B}=\frac{2 \pi \mathrm{mv}}{\mathrm{e}}$ and $\mathrm{K}=\mathrm{m}^{2} \pi \mathrm{vR} \mathrm{R}^{2}$
3 $\mathrm{B}=\frac{2 \pi \mathrm{mv}}{\mathrm{e}}$ and $\mathrm{K}=2 \mathrm{~m} \pi^{2} \mathrm{v}^{2} \mathrm{R}^{2}$
4 $\mathrm{B}=\frac{\mathrm{mv}}{\mathrm{e}}$ and $\mathrm{K}=\mathrm{m}^{2} \pi \mathrm{vR}^{2}$