The Circular Motion

Q.

A proton and an alpha particle both enter a region of uniform magnetic field $B$, moving at right angles to the field B. If the radius of circular orbits for both the particles is equal and the kinetic energy acquired by proton is 1 $MeV$, the energy acquired by the alpha particle will be

1. 4 $MeV$
2. 0.5 $MeV$
3. 1.5 $MeV$
4. 1 $MeV$

Q.

When a proton is released from rest in a room, it starts with an initial acceleration $a_0$ towards west. When it is projected towards north with a speed $v_0$, it moves with an initial acceleration $3a_0$ towards west. Find the electric field and the minimum possible magnetic field in the room.

Q. The force between two short electric dipole separated by a distance r is directly proportional to:

Q. An alpha particle is moving along X axis, enters into uniform electric field along y axis. The path if alpha particle i 1)straight line 2) elliptical 3) circular 4) parabolic Explain to me with reason.

Q.

A flat plate is moving normal to its plane through a gas under the action of a constant force $F$. The gas is kept at a very low pressure. The speed of the plate $v$ is much less than the average speed $u$ of the gas molecules. Which of the following options is/are true?

1. The resistive force experienced by the plate is proportional to $v$

2. At a later time the external force $F$ balances the resistive force

3. The plate will continue to move with constant non-zero acceleration, at all times

4. The pressure difference between the leading and trailing faces of the plate is proportional to $uv$

Q. A square loop of side $22\text{cm}$ is changed into a circle in $0.4\text{sec}$, inside a uniform magnetic field of $0.2\text{T}$. The emf induced is,

1. $6.6\text{mV}$
2. $3.3\text{mV}$
3. $1\text{mV}$
4. $13.2\text{mV}$

Q. Three particles, each having a charge of $10\mu C$ are placed at the corners of an equilateral triangle of side $10cm$. The electrostatic potential energy of the system is (Given $\frac{1}{4\pi {\epsilon }_0}=9\times {10}^{9}N{m}^2/C^2)$

1. Zero
2. Infinite
3. $27J$
4. $100J$

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 proton of mass $1.67\times {10}^{-27}$ kg and charge $1.6\times {10}^{-19}$ C is projected with a speed of $2\times {10}^6$m/s at an angle of ${60}^{\circ }$ to the X-axis. If a uniform magnetic field of 0.104 Tesla is applied along Y-axis, the path of proton is

1. A circle of radius = 0.2 m and time period $\pi \times {10}^{-7}s$
2. A circle of radius = 0.1 m and time period $2\pi \times {10}^{-7}s$
3. A helix of radius = 0.1 m and time period $2\pi \times {10}^{-7}s$
4. A helix of radius = 0.2 m and time period $4\pi \times {10}^{-7}s$

Q.

What is Stark Effect?

Q.

A charged particle moves through a magnetic field in a direction perpendicular to it , then which of the following quantities remains unchanged?

1. velocity

2. speed

3. acceleration

4. momentum

Q. A copper ball of density 8.6 $\frac{g}{c{m}^3}$, 1 cm in diameter is immersed in oil of density 0.8 $\frac{g}{c{m}^3}$. What is the charge in $\mu$C on the ball, if it remains suspended in an electric field of intensity 3600 $\frac{V}{m}$ acting in upward direction. (Answer the nearest integer)

Q.

Difference between conservative force and non conservative force ?

Q. A coil of mean area $500{\text{cm}}^2$ and having $1000\text{turns}$, is held perpendicular to a uniform magnetic field of $0.4\times {10}^{-4}\text{T}$. The coil is turned through ${180}^{\circ }$ in $\frac{1}{10}\text{seconds}$. Calculate the average induced emf?

1. $4\text{V}$
2. $0.4\text{V}$
3. $0.04\text{V}$
4. $0.8\text{V}$

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

Q. Two charged particles M and N enter a region of uniform magnetic field with velocities perpendicular to the field. The paths of particles are shown in Fig. The possible reason is

1. The charge of M is greater than that of N
2. The momentum of M is greater than that of N
3. The charge to mass ratio of M is greater than that of N
4. The speed of M is greater than that of N.

Q. A water droplet of mass $10\text{mg}$ and having a charge of $1.50\times {10}^{-6}\text{C}$ stays suspended in a room. What is the magnitude of electric field and its direction in the room ? (Take $g=10{\text{ms}}^{-2}$)

1. $30\text{N/C}$, downwards
2. $66.7\text{N/C}$, upwards
3. $132\text{N/C}$, upwards
4. $66.7\text{N/C}$, downwards

Q.

A beam of protons with speed $4\times {10}^5{\mathrm{ms}}^{-1}$ enters a uniform magnetic field of $0.3\mathrm{T}$at an angle of $60°$ to the magnetic field. The pitch of the resulting helical path of protons is close to: (Mass of the proton =$1.67\times {10}^{-27}\mathrm{kg}$, charge of the proton =$1.69\times {10}^{-19}\mathrm{C}$)

1. $4cm$

2. $2cm$

3. $12cm$

4. $5cm$

Q.

What would happen to the magnetic field lines if the current flowing through the conductor is reversed.

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

Q. A particle of mass m having a charge q enters into a circular region of radius R with velocity v directed towards the centre. The strength of magnetic field is B. Find the deviation in the path of the particle.

1. $\pi -ta{n}^{-1}\left(\frac{mv}{\frac{qBR}{2}}\right)$
2. $\pi -2ta{n}^{-1}\left(\frac{mv}{qBR}\right)$
3. $\pi +2ta{n}^{-1}\left(\frac{mv}{qBR}\right)$
4. $\pi +ta{n}^{-1}\left(\frac{mv}{qB{R}^2}\right)$

Q. A deutron of kinetic energy $50\text{keV}$ is describing a circular orbit of radius $0.5$ metre in a plane perpendicular to magnetic field $\overrightarrow{B}$. The kinetic energy of the proton that describes a circular orbit of radius $0.5$ metre in the same plane with the same $\overrightarrow{B}$ is

Q.

The unit of electric current “ampere” is the amount of current that is flowing through each of two parallel long wires 1 m apart will give rise to a force per unit length between them equal to

1. 1 N/m

2. 2 × 10^-7 N/m

3. 1 × 10^-2 N/m

4. 4π × 10^-7 N/m

Q. A vertical electric field of magnitude $4\times {10}^5\text{N/C}$ just prevents a water droplet of mass $1\times {10}^{-4}\text{kg}$ from falling. Find the charge on the droplet.

1. $1.5\times {10}^{-9}\text{C}$
2. $2.5\times {10}^{-9}\text{C}$
3. $3.5\times {10}^{-9}\text{C}$
4. $4.5\times {10}^{-9}\text{C}$

Q. When a coil of area $0.2{\text{cm}}^2$, having $30$ turns and whose plane is normal to the magnetic field is drawn out of the magnetic field, a charge of $1.5\times {10}^{-4}\text{C}$ flows in the circuit. If its resistance is $40\Omega$, then the magnetic flux density will be

1. $10\text{T}$
2. $0.1\text{T}$
3. $1\text{T}$
4. $0.01\text{T}$

Q.

A proton is moving along Z-axis in a magnetic field. The magnetic field is along X-axis. The proton will experience a force along

1. Z-axis

2. Negative Z-axis

3. Y-axis

4. X-axis

Q.

A particle of mass m and charge q is projected into a region having a perpendicular magnetic field B. Find the angle of deviation (figure 34.E14) of the particle as it comes out of the magnetic field if the width d of the region is very slightly smaller than

$\left(a\right)\frac{mv}{qB}\left(b\right)\frac{mv}{2qB}\left(c\right)\frac{2mv}{qB}$

Q. 42.Two large conducting plates are placed parallel to each other and they carry equal and opposite charges with surface density $ as shown in the figure . find the electric field in between the plates

Q. A star initially has ${10}^{40}$ deuterons. It produces energy via the processes,

${}_1{\text{H}}^2{+}_1{\text{H}}^2\to {}_1{\text{H}}^3+p$

${}_1{\text{H}}^2{+}_1{\text{H}}^3\to {}_2{\text{He}}^4+n$

The masses of the nuclei are as follows,

$m{(}_1{\text{H}}^2)=2.014\text{amu};m{(}_1{\text{H}}^3)=3.016\text{amu}m\left(p\right)=1.007\text{amu};m\left(n\right)=1.008\text{amu}m{(}_2{\text{He}}^4)=4.001\text{amu}$

If the average power radiated by the star is ${10}^{16}\text{W}$, the deuteron supply of the star is exhausted in a time period of the order of
[Take $1\text{amu}=931.5\frac{\text{MeV}}{c^2}$ ]

1. ${10}^6\text{s}$
2. ${10}^8\text{s}$
3. ${10}^{12}\text{s}$
4. ${10}^{16}\text{s}$

Q.

Magnetic field strength due to a short bar magnet on its axial line at a distance x is B. What is its value at the same distance on the equatorial line?

1. B

2. B/2

3. 2B

4. 4B