The Circular Motion

Q. Which particle will describe the smallest circle when projected with same velocity perpendicular to MF?

1. Electron
2. Proton
3. Helium ion
4. Lithium ion

Q. A long cylindrical wire have linear density $+2\times {10}^{-8}\text{C/m}$. An electron revolves around it in a circular path under the influence of the attractive electrostatic force. Find the kinetic energy of the electron.

1. $2\times {10}^{-17}\text{J}$
2. $3\times {10}^{-17}\text{J}$
3. $1\times {10}^{-17}\text{J}$
4. $4\times {10}^{-17}\text{J}$

Q. A charged particle (charge $q$, mass $m$) has velocity $v_0$ at the origin in +x direction. In space, there is a uniform magnetic field B in –z direction. Find the y coordinate of the particle when it crosses y axis.

1. $\frac{2m{v}_0}{qB}$
2. $\frac{m{v}_0}{qB}$
3. $\frac{4m{v}_0}{qB}$
4. None of these

Q. An uniformly charged thin ring has radius $10\text{cm}$ and total charge $12\text{nC}$. An electron is placed on the ring's axis at a distance $25\text{cm}$ from the centre of the ring and is constrained to stay on the axis of ring. The electron is then released from rest. Find the speed of electron when it reaches the center of the ring.

1. $$1.5\times {10}^4\text{m/s}$$
2. $$20\times {10}^4\text{m/s}$$
3. $$18\times {10}^5\text{m/s}$$
4. $$15.45\times {10}^6\text{m/s}$$

Q. Two point charges $+10\text{nC}$ and $-10\text{nC}$ are separated by a distance of $6\text{cm}$. Find the electric flux hrough a circle of radius $4\text{cm}$ placed with its centre coinciding with the mid - point of line joining the two charges in the perpendicular plane as shown in the figure.

1. $542.2{\text{N-m}}^2/\text{C}$
2. $742{\text{N-m}}^2/\text{C}$
3. $642{\text{N-m}}^2/\text{C}$
4. $442.4{\text{N-m}}^2/\text{C}$

Q. A charged particle is undergoing a circular motion in a uniform magnetic field, now speed of particle is doubled, then

1. Radius remains same.
2. Angular speed remains same.
3. Time period becomes half.
4. Magnetic force becomes half.

Q. A charge (q, m) is projected perpendicular away from an infinitely long wire carrying a current i with a speed $v_0$. Find the maximum separation between the charge and the wire in the subsequent motion if the initial separation is $x_0$.

1. $3x_0$
2. $x_0{e}^{\frac{\pi m{v}_0}{{\mu }_{0}iq}}$
3. $x_0{e}^{\frac{2\pi m{v}_0}{{\mu }_{0}iq}}$
4. $2x_0$

Q. A charged particle (q, m) is projected along y-axis in a uniform magnetic field directed along z-axis. A viscous force $\overrightarrow{f}=-b\overrightarrow{v}$ also acts on particle(where $\overrightarrow{v}$ is the velocity of the particle).

1. Path of the particle will be spiral inward.
2. Particle will stop after travelling a distance of $\frac{m{v}_0}{b}$.
3. Time required to travel the distance of $\frac{m{v}_0}{b}$ is $\frac{zm}{b}$.
4. Velocity of the particle decreases linearly

Q. A charged particle (q, m) is projected along y-axis in a uniform magnetic field directed along z-axis. A viscous force $\overrightarrow{f}=-b\overrightarrow{v}$ also acts on particle(where $\overrightarrow{v}$ is the velocity of the particle).

1. Path of the particle will be spiral inward.
2. Particle will stop after travelling a distance of $\frac{m{v}_0}{b}$.
3. Time required to travel the distance of $\frac{m{v}_0}{b}$ is $\frac{zm}{b}$.
4. Velocity of the particle decreases linearly

Q. A charged particle (charge $q$, mass $m$) has velocity $v_0$ at the origin in +x direction. In space, there is a uniform magnetic field B in –z direction. Find the y coordinate of the particle when it crosses y axis.

1. $\frac{2m{v}_0}{qB}$
2. $\frac{m{v}_0}{qB}$
3. $\frac{4m{v}_0}{qB}$
4. None of these

Q. A particle moves in a region having a uniform magnetic field and a parallel, uniform electric field. At some instant, the velocity of the charged particle is perpendicular to the field direction. The path of the particle will be

1. a straight line
2. a circle
3. a helix with a uniform pitch
4. a helix with a non-uniform pitch.