Analysis of Force Equation

Q. Two equal charges are separated by a distance d. A third charge placed on a perpendicular bisector at x distance will experience maximum coulomb force when

1. $x=\frac{d}{2\sqrt{2}}$
2. $x=\frac{d}{\sqrt{2}}$
3. $x=\frac{d}{2}$
4. $x=\frac{d}{2\sqrt{3}}$

Q.

A charged particle of mass m and charge q is released from rest in an electric field of constant magnitude E. The kinetic energy of the particle after time t is

Q.

An electric dipole of length $2cm$, when placed with its axis making an angle of $\theta =60$ with a uniform electric field, experiences a torque of $8\sqrt{3}Nm$. Calculate the potential energy of the dipole, if it has a charge of $\pm 4nC.$

Q. A particle with ${10}^{-11}$ coulomb of charge and ${10}^{-7}$ kg mass is moving with a velocity of ${10}^8$ m/s along the y-axis. A uniform static magnetic field B = 0.5 T is acting along the x-direction. The force on the particle is

1. $5\times {10}^{-4}Nalong-\hat{k}$
2. $5\times {10}^{-11}Nalong\hat{i}$
3. $5\times {10}^{3}Nalong\hat{k}$
4. $5\times {10}^{-11}Nalong\hat{j}$

Q.

Two streams of photons, possessing energies equal to twice and ten times the work function of metal are incident on the metal surface successively. The value of the ratio of maximum velocities of the photoelectrons emitted in the two respective cases is $x:3$. The value of x is ________.

Q.

Define induced EMF.

Q.

Explain the discovery of electrons?

Q. A 2 MeV proton is moving perpendicular to a uniform magnetic field of 2.5 T. The force on the proton is (mass of proton = $1.6\times {10}^{-27}kg$)

1. $10\times {10}^{-12}N$
2. $8\times {10}^{-12}N$
3. $8\times {10}^{-11}N$
4. $2.5\times {10}^{-10}N$

Q.

A solid sphere of radius $R$ carries a charge $Q+q$ distributed uniformly over its volume. A very small point-like piece of it of mass $m$ gets detached from the bottom of the sphere and falls down vertically under gravity. This piece carries charge $q$. If it acquires a speed v when it has fallen through a vertical height $y$ (see figure), then : (assume the remaining portion to be spherical).

1. $v^2=2y\left[\frac{qQ}{4\pi {\epsilon }_{0}R\left(R+y\right)m}+g\right]$

2. $v^2=2y\left[\frac{QqR}{4\pi {\epsilon }_0{\left(R+y\right)}^{3}m}+g\right]$

3. $v^2=y\left[\frac{qQ}{4\pi {\epsilon }_{0}R\left(R+y\right)m}+g\right]$

4. $v^2=y\left[\frac{qQ}{4\pi {\epsilon }_0{R}^{2}ym}+g\right]$

Q. A non-conducting solid sphere of radius R is uniformly charged. The magnitude of the electric field due to the sphere at a distance from its centre

1. Increases as r increases for r < R
2. Decreases as r increases for $0<r<\infty$
3. Decreases as r increases for $R<r<\infty$
4. Is discontinuous at r = R

Q. A thin non conducting disc of radius $R$ is rotating clockwise as shown in figure with an angular velocity $\omega$ about its central axis, which is perpendicular to its plane. Both of its surfaces carry $+ve$ charges of uniform surface charge density. Half of the disc is in a region of uniform unidirectional magnetic field parallel to the plane of disc, as shown. Then identify the correct statement:

1. The net torque on the disc is zero
2. The net torque on the disc is directed leftwards
3. The net torque on the disc is directed rightwards
4. The net torque on the disc is parallel to $B$.

Q. A coil having N turns is wound tightly in the form of a spiral with inner and outer radii a and b respectively. When a current I passes through the coil, the magnetic field at the centre is

1. $\frac{{\mu }_{0}NI}{b}$
2. $\frac{2{\mu }_{0}NI}{a}$
3. $\frac{{\mu }_{0}NI}{2(b-a)}ln\frac{b}{a}$
4. $\frac{{\mu }_0{I}^N}{2(b-a)}ln\frac{b}{a}$

Q. A thin circular wire of radius r has a charge Q If a point charge q is placed at the centre of the ring, then what is the increase in the tension in the wire. Click here to view details:

Q.

Can the electric field be negative?

Q. Consider the situation shown in the figure. The wire $\text{AB}$ is sliding on the rails with a constant velocity. If the wire is replaced by a semicircular wire, then

1. Emf induced in the circuit will increase.
2. Emf induced in the circuit will remain the same.
3. The direction of induced current will reverse.
4. The direction of induced current will remain the same.
   

Q. A semicircular wire $PQ$ of radius $R$ is moved with a velocity $v$ in a transverse magnetic field, as shown in the figure. The value of induced emf across the ends of the wire is -

1. $\pi BRv$ with the end $P$ at higher potential
2. $\pi BRv$ with the end $P$ at lower potential
3. $2BRv$ with the end $Q$ at higher potential
4. $2BRv$ with the end $Q$ at lower potential

Q. An electron moves with speed $2\times {10}^{5}m/s$ along the positive x-direction in the presence of a magnetic induction $B=\hat{i}+4\hat{j}-3\hat{k}$ (in Tesla.) The magnitude of the force experienced by the electron in Newton's is (charge on the electron = $1.6\times {10}^{-19}$ C)

1. $1.18\times {10}^{-13}$ N
   
2. $1.28\times {10}^{-13}$ N
   
3. $1.6\times {10}^{-13}$ N
   
4. $1.72\times {10}^{-13}$ N

Q. Three equal negative charges, $-q_1$ each, form the vertices of an equilateral triangle. A particle of mass $m$ and a positive charge $q_2$ is constrained to move along a line perpendicular to the plane of triangle and through its centre which is at a distance $r$ from each of the negative charges as shown in the figure. The whole system is kept in gravity free space. Find the time period of vibration of the particle for small displacement from equilibrium position.

1. $2\pi \sqrt{\frac{4\pi {ϵ}_{0}m{r}^3}{3q_1{q}_2}}$
2. $2\pi \sqrt{\frac{4\pi {ϵ}_{0}m{r}^3}{q_1{q}_2}}$
3. $2\pi \sqrt{\frac{3\pi {ϵ}_{0}m{r}^3}{4q_1{q}_2}}$
4. $2\pi \sqrt{\frac{\pi {ϵ}_{0}m{r}^3}{3q_1{q}_2}}$

Q. An electron at rest is accelerated by a potential $V_1$ and it experiences a force ‘F’ in a uniform magnetc field.When it is accelerated by a potential $V_2$ the electron experiences a force 2F in the same field. The value of $\frac{V_1}{V_2}$ is

1. $\frac{1}{2}$
2. $\frac{1}{4}$
3. 2
4. 4

Q. An electron gun is placed inside a long solenoid of radius $R$ on its axis. The solenoid has $n$ turns per length and carries a current $I$. The electron gun shoots an electron along the radius of the solenoid with speed $v$. If the electron does not hit the surface of the solenoid, maximum possible value of $v$ is
(all symbols have their standard meaning):

1. $\frac{e{\mu }_{0}nIR}{m}$
2. $\frac{e{\mu }_{0}nIR}{2m}$
3. $\frac{e{\mu }_{0}nIR}{4m}$
4. $\frac{2e{\mu }_{0}nIR}{m}$

Q. A wire having a uniform linear charge density $\lambda$, is bent in the form of a ring of radius $R$. Point $A$ as shown in the figure, is in the plane of the ring but not at the centre. Two elements of the ring of lengths $a_1$ and $a_2$ subtend same (very small) angle at the point $A$. If they are at distances $r_1$ and $r_2$ from the point $A$ respectively, choose the correct statements.

1. The ratio of charge of elements $a_1$ and $a_2\text{is}\frac{r_1}{r_2}.$
2. The element $a_1$ produced greater magnitude of electric field at $A$ than element $a_2$.
3. The elements $a_1$ and $a_2$ produce same potential at $A$.
4. The direction of net electric field at $A$ is towards element $a_2$.

Q. An ionised gas contains both positive and negative ions. If it is subjected simultaneously to an electric field along the +ve x-axis and a magnetic field along the +z direction then

1. Positive ions deflect towards – y direction and negative ions towards + y direction.
2. Positive ions deflect towards +y direction and negative ions towards – y direction
3. All ions deflect towards + y direction
4. All ions deflect towards – y direction

Q. 1.5 mW of 4000 Å light is directed at a photoelectric cell. If 0.10 per cent of the incident photons produce, photoelectrons, find the current in the cell. [Given: h = 6.6 × 10–34 J-s, c = 3 × 108 m/s and e = 1.6 × 10–19 C] Options: 0.12 μA 0.24 μA 0.36 μA 0.48 μA

Q.

A particle having mass m and charge q is released from the origion in a region in which electric field and magnetic field are given by

$\overrightarrow{B}=-B_0\overrightarrow{J}$ and $\overrightarrow{E}=E_o\overrightarrow{K.}$

Find the speed of the particle as a function of its z-coordinate.

Q.

A charged particle moves with velocity $\overrightarrow{v}$ in a uniform magnetic field $\overrightarrow{B}$. The force experienced by the particle is

1. Never zero

2. Always zero

3. Zero if $\overrightarrow{v}$and $\overrightarrow{B}$ are parallel

4. Zero if $\overrightarrow{v}$and $\overrightarrow{B}$ are perpendicular

Q. A conducting rod of length $l$ is moved with a constant velocity $\overrightarrow{v}$ in a magnetic field $\overrightarrow{B}$. A potential difference appears across the two ends

1. If $\overrightarrow{v}||\overrightarrow{l}$
2. If $\overrightarrow{v}||\overrightarrow{B}$
3. If $\overrightarrow{l}||\overrightarrow{B}$
4. None of these

Q. A uniform magnetic field, $\overrightarrow{B}=(3\hat{i}+4\hat{j}+5\hat{k})\text{T}$, exists in a region. A rod of length $5\text{m}$, placed along $y-$axis, is moved along $x-$axis with constant speed of $1{\text{ms}}^{-1}$. The magnitude of induced emf in the rod is -

1. Zero
2. $25\text{V}$
3. $5\text{V}$
4. $10\text{V}$

Q. Two point charges $q$ and $-q$ are at positions $(0,0,d)$ and $(0,0,-d)$ respectively. What will be the electric field at point $(a,0,0)$ due to both the charges?

1. $\frac{2kqd}{4\pi {\in }_0(d^2+a^2{)}^{3/2}}\hat{k}$
2. $\frac{qd}{4\pi {\in }_0(d^2+a^2{)}^{3/2}}\hat{k}$
3. $\frac{-2kqd}{4\pi {\in }_0(d^2+a^2{)}^{3/2}}\hat{k}$
4. $\frac{-kqd}{4\pi {\in }_0(d^2+a^2{)}^{3/2}}\hat{k}$

Q. In an experiment on photoelectric effect, light of wavelength $400\text{nm}$ is incident on a caesium plate at the rate of $5.0\text{W}$. The potential of the collector plate is made sufficiently positive with respect to the emitter so that the current reaches its saturation value. Assuming that on the average, one out of every ${10}^6$ photons is able to eject a photoelectron, find the photocurrent in the circuit.
[Use $hc=1240\text{eV (nm)}$]

1. $3.2\mu \text{A}$
2. $1.6\mu \text{A}$
3. $4.8\mu \text{A}$
4. $6\mu \text{A}$

Q.

The radii of a spherical capacitor are equal to a and b(b > a). The space between them is filled with a dielectric of dielectric constant K and resistivity $\rho$. At t = 0, the inner electrode is given a charge $q_0$. The Charge q on the inner electrode as a function of time is given by $q=q_0{e}^{-\frac{t}{N\rho K{\epsilon }_0}};$ then N is___