Desciption of Force

Q.

A particle of mass m and carrying charge -q_{​​​​​1 is moving around a charge:+q}​​​​_{​​​​​​2 along a circular path of radius r.find period of revolution of charge}

Q. A charged particle $\left(\text{mass}m\text{and}\text{charge}q\right)$ moves along $x-\text{axis}$ with velocity $v_0$. When it passes through the origin, it enters a region having uniform electric field $E=-E\hat{j}$ which extends up to $x=d$. The equation of path of electron in the region $x>d$ is :

1. $y=\frac{qEd}{m{v}_0^2}(x-d)$
2. $y=\frac{qEd}{m{v}_0^2}(\frac{d}{2}-x)$
3. $y=\frac{qEd}{m{v}_0^2}x$
4. $y=\frac{qE{d}^2}{m{v}_0^2}x$

Q.

A particle of mass m and charge (−q) enters the region between the two charged plates initially moving along x-axis with speed vx (like particle 1 in Fig. 1.33). The length of plate is L and an uniform electric field E is maintained between the plates. Show that the vertical deflection of the particle at the far edge of the plate is qEL²/ (2m).

Compare this motion with motion of a projectile in gravitational field discussed in Section 4.10 of Class XI Textbook of Physics.

Q.

Figure 1.33 shows tracks of three charged particles in a uniform electrostatic field. Give the signs of the three charges. Which particle has the highest charge to mass ratio?

Q. A circular ring of radius $R$ with uniform positive charge density $\lambda$ is fixed in the $y-z$ plane with its centre at the origin $O$. A particle of mass $m$ and charge $+q$ is projected from point $P$ $(\sqrt{3}R,0,0)$ on the positive $x$-axis directly towards $O$ with initial velocity $v$ such that the particle does not come back to $P$. The minimum value of $v$ is

1. $\sqrt{\frac{3q\lambda }{2{ϵ}_{0}m}}$
2. $\sqrt{\frac{2q\lambda }{{ϵ}_{0}m}}$
3. $\sqrt{\frac{q\lambda }{2{ϵ}_{0}m}}$
   
4. $\sqrt{\frac{q\lambda }{{ϵ}_{0}m}}$
   

Q. A charged particle with charge $q$ enters a region of constant, uniform and mutually orthogonal fields $\overrightarrow{E}$ and $\overrightarrow{B}$ , with a velocity $\overrightarrow{v}$ perpendicular to both $\overrightarrow{E}$ and $\overrightarrow{B}$, and comes out without any change in magnitude or direction of $\overrightarrow{v}$. Then

1. $\overrightarrow{v}=\frac{\overrightarrow{E}\times \overrightarrow{B}}{B^2}$
2. $\overrightarrow{v}=\frac{\overrightarrow{E}\times \overrightarrow{E}}{B^2}$
3. $\overrightarrow{v}=\frac{\overrightarrow{E}\times \overrightarrow{B}}{E^2}$
4. $\overrightarrow{v}=\frac{\overrightarrow{B}\times \overrightarrow{B}}{E^2}$

Q. A hollow conducting sphere of radius $R$ and total charge $q$ rotates about its diametrical axis with constant angular speed $\omega$. The magnitude of magnetic moment of the sphere is :

1. $\frac{1}{3}q{R}^2\omega$
2. $\frac{2}{3}q{R}^2\omega$
3. $\frac{1}{5}q{R}^2\omega$
4. $\frac{2}{5}q{R}^2\omega$

Q. Protons are projected with an initial speed, $u={10}^4\text{m/s}$ into a region where a uniform electric field $\overrightarrow{E}=-720\hat{j}\text{N/C}$ is present, as shown in figure. The protons are to hit a target that lies at a horizontal distance of $1.3\text{mm}$ from the point where the protons are launched. Find the total time of flight for $\theta ={37}^{\circ }$.

1. $0.7\times {10}^{-7}\text{s}$
2. $1.7\times {10}^{-7}\text{s}$
3. $2.7\times {10}^{-7}\text{s}$
4. $3.7\times {10}^{-7}\text{s}$

Q. A point charge $4\mu C$ is placed at x = 0 and another point charge $-6\mu C$ is placed at x = 40 cm. If a third point charge is placed so that it experiences zero net force, its distance from the origin is nearly equal to

1. 2 m on the negative x-axis
2. 2m on the positive x-axis
3. 20 cm on the positive x-axis
4. 20 cm on the negative x-axis

Q. Two charged balls are attached by silk threads of length $l$ to the same point. Their velocity is $\frac{K}{\sqrt{x}}$, where $K$ is a constant and $x$ is the distance between the balls, $x$ is very small in comparison to $l$. The rate of leakage of charge in ${10}^{-5}\text{C/s}$ is (take $\frac{l}{mg}=10,K=4\sqrt{2}$)

1. ${10}^{-5}\text{C/sec}$
2. $2\times {10}^{-5}\text{C/sec}$
3. $3\times {10}^{-5}\text{C/sec}$
4. ${10}^{-3}\text{C/sec}$

Q. 146.If 1 coulumb charge is placed at the centre of cube of side 10 cm calculate the flux coming out of any face of the cube?

Q.

An alpha particle is projected vertically upward with a speed of $3.0\times {10}^4$ km $s^{-1}$ in a region where a magnetic field of magnitude 1.0 T exists in the direction south to north. Find the magnetic force that acts on the $\alpha -$ particle.

Q.

At what ponts dipole field intensity is parallel to the line joining the charges?

Q.

A charged particle is released from rest in a region of steady uniform electric and magnetic fields which are parallel to each other. The particle will move in a

1. Straight line

2. Circle

3. Helix

4. Cycloid

Q. Two small balls having the same mass and charge are located on the same vertical at height H1 and H2 are thrown in the same direction along the horizontal at the same velocity V. the first ball touches the ground at l distance from the initial vertical at what height will the second ball be at that this instant

Q. An electron having charge $e$ and mass $m$ at rest starts from the lower plate of two metallic plates separated by a distance $d$. If the potential difference between the plates is $V$, the time taken by the electron to reach the upper plate is

1. $\sqrt{\frac{2m{d}^2}{eV}}$
2. $\sqrt{\frac{m{d}^2}{eV}}$
3. $\sqrt{\frac{m{d}^2}{2eV}}$
4. $\sqrt{\frac{4m{d}^2}{eV}}$

Q. Consider two points 1 and 2 in a region outside a charged sphere. Two points are not very far away from the sphere. If E and V represent the electric field vector and the electric potential, which of the following is not possible

1. $|\dot{E_1}|=|\dot{E_2}|,V_1\ne V_2$
2. $\stackrel{\rightharpoondown }{E_1}\ne \stackrel{\rightharpoondown }{E_2},V_1\ne V_2$
3. $\stackrel{\rightharpoondown }{E_1}\ne \stackrel{\rightharpoondown }{E_2},V_1=V_2$
4. $|\dot{E_1}|=|\dot{E_2}|,V_1=V_2$

Q. A charged particle goes undeflected in a region containing electric and magnetic fields. It is possible that

1. $\overrightarrow{E}||\overrightarrow{B},\overrightarrow{V}||\overrightarrow{E}$
2. $\overrightarrow{E}$ is not parallel to $\overrightarrow{B}$
3. $\overrightarrow{V}||\overrightarrow{B},\overrightarrow{E}$ is not parallel to $\overrightarrow{B}$
4. $\overrightarrow{E}||\overrightarrow{B}$, but $\overrightarrow{V}$ is not parallel to $\overrightarrow{B}$

Q. In a certain region, uniform electric field exists as $\overrightarrow{E}=E_0\hat{j}.$ A proton and an electron are projected from origin at time $t=0$ with certain velocities along $+x$-axis direction. Due to the electric field, they experience force and move in the $xy$-plane along different trajectories.

$\left(iii\right)$ If they have the same initial velocity then for the same displacement along $x$ axis, displacement along $y$ axis is

1. more for proton
2. more for electron
3. equal for both
4. independent of kinetic energy

Q. A proton of mass m and charge +e is moving in a circular orbit of a magnetic field with energy 1MeV. What should be the energy of $\alpha$ -particle (mass = 4 m and charge = +2e), so that it can revolve in the path of same radius?

1. 1 MeV​
2. 4 MeV​
3. 2 MeV​
4. 0.5 MeV​

Q. An electron flies into a homogeneous magnetic field perpendicular to the lines of force. The velocity of electron is $4\times {10}^{7}m{s}^{-1}$ and induction of field is ${10}^{-3}$T. The tangential and normal accelerations of electron are

1. $0,7\times {10}^{15}m{s}^{-2}$
2. $7\times {10}^{15}m{s}^{-2},0$
3. $5\times {10}^{15}m{s}^{-2},0$
4. $3\times {10}^{15}m{s}^{-2},0$

Q.

A potential difference of 600 V is applied across the plates of a parallel plate capacitor. The separation between the plates is 3 mm. An electron projected parallel to the plates as shown with a speed of 2×10⁶ m^-1 moves undeflected between the plates. The magnitude and direction of the magnetic field is

1. 0.2 T, into the page

2. 0.2 T, out the page

3. 1 T, into the page

4. 0.1 T, out of the page

Q. An electric field of magnitude $1000\text{N/C}$ is produced between two parallel plates having a separation of $2.0\text{cm}$ as shown in figure. With what minimum speed should an electron be projected from the lower plate in the direction of the field so that it may just reach the upper plate ?
(Assume gravity free space)
(Charge on electron is $-1.6\times {10}^{-19}\text{C}$ and mass of electron is $9.1\times {10}^{-31}\text{kg}$)

1. $1.7\times {10}^6\text{m/s}$
2. $2.7\times {10}^6\text{m/s}$
3. $3.7\times {10}^6\text{m/s}$
4. $4.7\times {10}^6\text{m/s}$

Q. A non-relativistic positive charge particle of charge $q$ and mass $m$ is projected perpendicular to uniform magnetic field $B$ as shown. Neglecting gravity, calculate $x-$coordinate of point on screen at which the charge particle will hit : $d=\frac{R\sqrt{3}}{2}$, where $R=\frac{mV}{qB}$

1. $\sqrt{3}R$
2. $2R$
3. The particle describes a helical path of radius $R=\frac{mv\sin \alpha }{qB}$
4. The particle describes a circular path of radius $R=\frac{mv}{qB}$

Q. An electron is moving along positive x-axis. To get it moving on an anticlockwise circular path in x-y plane, a magnetic filed is applied?

1. Along negative y-axis
2. Along negative z-axis
3. Along positive y-axis
4. Along positive z-axis

Q. At some instant the velocity component of an electron moving between two charged parallel plates are $u_x=1.5\times {10}^5\text{m/s}$ and $u_y=3\times {10}^6\text{m/s}$. Suppose that the electric field between the plates is given by $\overrightarrow{E}=120\hat{j}\text{N/C}$. What will be the velocity of the electron as its $x-$coordinate changes by $2\text{cm}$?
(Neglect gravity)

1. $(1.5\hat{i}+2\hat{j})\times {10}^5\text{m/s}$
2. $(2\hat{i}+1.5\hat{j})\times {10}^5\text{m/s}$
3. $(1.5\hat{i}-2\hat{j})\times {10}^5\text{m/s}$
4. $(2\hat{i}-1.5\hat{j})\times {10}^5\text{m/s}$

Q. Protons are projected with an initial speed, $u={10}^4\text{m/s}$ into a region where a uniform electric field $\overrightarrow{E}=-720\hat{j}\text{N/C}$ is present, as shown in figure. The protons are to hit a target that lies at a horizontal distance of $1.3\text{mm}$ from the point where the protons are launched. Find the total time of flight for $\theta ={37}^{\circ }$.

1. $0.7\times {10}^{-7}\text{s}$
2. $1.7\times {10}^{-7}\text{s}$
3. $2.7\times {10}^{-7}\text{s}$
4. $3.7\times {10}^{-7}\text{s}$

Q. A charged particle is released from rest in a region of uniform electric field and magnetic field, which are parallel to each other. The locus of the particle will be

1. helix of constant pitch
2. cycloid
3. helix of varrying pitch
4. straight line

Q. A charged particle goes undeflected in a region of space containing an electric field $\overrightarrow{E}$ and a magnetic field of intensity $\overrightarrow{B}$. Which of the following is possible?

1. $\overrightarrow{E}$ is parallel to $\overrightarrow{B}$ but $\overrightarrow{v}$ is perpendicular to $\overrightarrow{E}$
2. $\overrightarrow{E}$ is parallel to $\overrightarrow{B}$ and $\overrightarrow{v}$ parallel to $\overrightarrow{E}$
3. $\overrightarrow{E}$ is perpendicular to $\overrightarrow{B}$ and $\overrightarrow{v}$ is parallel to $\overrightarrow{E}\times \overrightarrow{B}$
4. $\overrightarrow{E}$ is perpendicualar to $\overrightarrow{B}$ and $\overrightarrow{v}$ is parallel to $\overrightarrow{E}.\overrightarrow{B}$

Q. Answer the following questions.
(i) An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why is it so?
(ii) Explain why two field lines never cross each other at any point.