Chapter 23

Two uncharged thin and small metal rods \(x\) and \(y\) are placed near a non- conducting sheet s of uniform charge density \(\sigma\), then : (a) \(s\) attracts both \(x\) and \(y\) (b) \(x\) attracts both \(s\) and \(y\) (c) \(y\) attracts both \(s\) and \(x\) (d) all of the above

Five balls, numbered 1 to 5 are suspended using separate threads. Pairs \((1,2),(2,4),(4,1)\) show electrostatic attraction; while pairs \((2,3)\) and \((4,5)\) show repulsion therefore, ball 1 must be : (a) positively charged (b) negatively charged (c) neutral (d) made of metal

A sure test of electrification is: (a) attraction (b) repulsion (c) friction (d) induction

Two metallic spheres carry equal charges. The distance between the spheres cannot be considered large in comparison with the diameters of the spheres. In which case, will the force of interaction between the spheres be creater? Like charges (o, Unlike charges (c) One is neutral and other is charged (d) None of the above

Mark correct option or options: (a) The electric charge without mass is possible (b) The charge without mass is not possible (c) The electric charge may be transferred without transferring mass (d) Mass without electric charge is not possible

In relativistic mechanics \(m=\frac{m_{0}}{\sqrt{\left(1-\frac{v^{2}}{c^{2}}\right)}}\) the equivalent relation in electricity for elzctric charge is: (a) \(q=q_{0}\) (b) \(q=\frac{q_{v}}{\sqrt{\left(1-\frac{v^{2}}{c^{2}}\right)}}\) (c) \(q_{0}=\frac{q}{\sqrt{\left(1-\frac{v^{2}}{c^{2}}\right)}}\) (d) \(q=\frac{q_{0} v}{c}\)

Mark correct option or options: (a) Like charged bodies always repel each other (b) Like charged bodies always attract each other (c) Like charged bodies may attract each other (d) None of the above

A particle with positive charge \(Q\) is held fixed at the origin. A second particle with positive charge \(q\) is fired at the first particle and follows a trajectory as shown (assume region 9 to be gravity free): (a) Angular momentum of the point charge \(q\) about \(O\) remains constant during motion (b) The torque of electrostatic force on point charge \(q\) about origin is non- zero (c) (a) and (b) are correct (d) (a) and (b) are wrong

The charge conservation principle is : (a) only applicable when charges are in rest (b) only applicable when charges are in motion (c) not applicable in nuclear reaction (d) applicable in nuclear reaction

Coulomb's law is applicable to: (a) point charges (b) spherical charges (c) like charges (d) all of these

Two identically charged spheres when suspended by strings of equal lengths make an angle of \(30^{\circ}\) with each other. When they are immersed in a liquid of density less than the density of the material of the sphers. (a) the electric force between them increases (b) the electric force between them decreases (c) the net downward force will increase (d) the net downward force will remain unchanged

Two positively charged particles each having charge \(Q\) are \(d\) distance apart. A third charge is introduced in midway on the line joining the two. Find nature and magnitude of third charge, so that the system is in equilibrium : (a) \(q=\frac{-Q}{4}\) (b) \(q=\frac{Q}{4}\) (c) \(q=\frac{3 Q}{4}\) (d) \(q=\cdots \frac{3 Q}{4}\)

Two negative charges of unit magnitude and a positive charge \(q\) are placed along a straight line. The charge \(q\) is placed between negative charges as such the system of charges is in equilibrium. This system is in : (a) stable equilibrium for the displacement of charge \(q\) in the normal direction of line joining the negative charges (b) unstable equilibrium for the displacement of charge \(q\) in the normal direction of line joining the negative charges (c) stable equilibrium for the displacement of charge \(q\) in the direction of line joining the negative charges (d) neutral equilibrium for the displacement of charge \(q\) along the line joining the negative charges

Two identical pendulums \(A\) and \(B\) are suspended from the same point. The bobs are given positive charges, with \(A\) having more charge than \(B\). They diverge and reach at equilibrium, with \(A\) and \(B\) making angles \(\theta_{1}\) and \(\theta_{2}\) with the vertical respectively : (a) \(\theta_{1}>\theta_{2}\) (b) \(\theta_{1}<\theta_{2}\) (c) \(\theta_{1}=\theta_{2}\) (d) the tension in \(A\) is greater than that in \(B\)

Two balls of same radius and mass are suspended on threads of length \(1 \mathrm{~m}\) as shown. The mass of each ball and charge is \(15 \mathrm{~g}\) and \(126 \mu \mathrm{C}\) respectively. When the balls are in equilibrium, the separation between them is \(8 \mathrm{~cm}\). The new saparation between them when one of the balls is discharged to half of original charge, is: (a) \(5 \mathrm{~cm}\) (b) \(6 \mathrm{~cm}\) (c) \(4 \mathrm{~cm}\) (d) \(2 \mathrm{~cm}\)

Mark correct option or options: (a) A point charge can not exert force on itself (b) Coulomb's force is stronger than the gravitational force (c) Electric field can exist only in material medium (d) None of the above

A negatively charged metallic ball is supported on a rigid insulating stand. We wish to measure the electric field \(E\) at a point \(P\) in the same horizontal level as that of the metallic ball. To do so, we put a positive charge \(q_{0}\) and measure \(F / q_{0}\). The electric field at the point \(P\) is: (a) \(=\frac{F}{q_{0}}\) (b) \(<\frac{F}{a_{0}}\) (c) \(>\frac{F}{q_{0}}\) (d) none of these

Two bodies \(A\) and \(B\) of definite shape are placed near one another. Electrostatic attraction is found between thebodies, then: (a) both bodies must be positively charged (b) both bodies must be negatively charged (c) both bodies must be oppositely charged (d) body \(A\) may be neutral

If \(\sigma=\) surface charge density, \(\varepsilon=\) electric permittivity, the dimensions of \(\frac{\sigma}{\varepsilon}\) are same as: (a) electric force (b) electric field intensity (c) pressure (d) electric charge

Four equal positive charges each of magnitude \(q\) are placed at the respective vertices of a square of side length 1\. A point charge \(Q\) is placed at the centre of the square. Then : (a) \(Q\) must not be in equilibrium (b) \(Q\) must be in stable equilibrium (c) \(Q\) must be in neutral equilibrium (d) \(Q\) must be in unstable equilibrium

Two small particles \(A\) and \(B\) of equal masses carrying equal positive charges are attached to the ends of a nonconducting light thread of length \(2 l .\) A particle \(C\) of mass twice of \(A\) is attached at mid-point of thread. The whole system is placed on a smooth horizontal floor and the particle \(C\) is given a velocity \(v\) as shown in the figure. Which of following statements is correct ? (a) The velocity of centre of mass of the system will remain constant during motion (b) At the instant of minimum separation between \(A\) and \(B\), there is no approach velocity between them or velocities of three particles are identical (c) The velocity of centre of mass of the system will be \(v / 2\) (d) All of the above

Two small identical balls \(A\) and \(B\) lying on a horizontal smooth plane are connected by a massless spring. Ball \(A\) is fixed but ball \(B\) is free to move. When both balls are charged identically, then:(a) at the time of maximum separation between balls, magnitude of acceleration will be maximum (b) at the equilibrium position of \(B\), velocity of ball \(B\) will be maximum (c) the ball \(B\) executes simple harmonic motion (d) all of the above

For the metallic conductor: (a) dielectric constant must be zero (b) dielectric constant must not be infinity (c) dielectric constant must be infinity (d) dielectric constant may be infinity

A dimensionless body having a physical quantity varies as \(1 / r^{2}\), where \(r\) is distance from the body. This physical quantity may be : (a) gravitational potential (b) electric field (c) gravitational fiot, (d) none of the aboue

If two charged particles of same mass and charge are projected in a uniform electric field with the same speed, then: (a) both have same momentum at any instant (b) both have same kinetic energy at any instant (c) both have same magnitude of momentum at any instant (d) they may move on a straight line

A particle having charge \(q\) and mass \(m\) is projected in uniform electric field \(E\) with speed \(u\) making angle \(\theta=30^{\circ}\) with electric field : (a) If the gravitational field is present, the path may be straight line (b) If the gravitational field is absent, the path may be circle (c) If the gravitational field is absent, the path may not be parabola (d) If the gravitational field is absent, the path may not be straight line

A positive charge \(q\) is located at a point. What is the work done if an electron is carried once completely around this charge along a circle of radius \(r\) about this point charge \(q ?\) \((a) \geq 0\) (b) \(=0\) (c) \(<0\) (d) \(>0\)

Two points charges \(+q_{1}\) and \(+q_{2}\) are placed at a certain distance apart, then: (a) they produce the same electric field on each other (b) they exert same forces on each other (c) for minimum force between them, the magnitude of each charge must be equal to \(1.6 \times 10^{-19} \mathrm{C}\) (d) all of the above

An electrostatic field \(E\) of magnitude \(10 \mathrm{~N} / \mathrm{C}\) is directed along positive \(x\) -axis. A point charge of \(10^{-6} \mathrm{C}\) is shifted from \(A(1 \mathrm{~m}, 0)\) to \(B(2 \mathrm{~m}, 0,1 \mathrm{~m})\), then from point \(B\) to \(C(0,0,0)\), the work done by electrostatic force is: (a) \(-10^{-5} \mathrm{~J}\) (b) \(10^{-5} \mathrm{~J}\) (c) \(-10^{-4} \mathrm{~J}\) (d) none of these

The electric field inside a conductor: (a) must be zero (b) may be non-zero (c) must be non-zero (d) (a) and (c) are correct

If a conductor encloses a charge, then in equilibrium: (a) its inner surface will have an opposite charge equal in magnitude to the charge enclosed (b) its inner surface has no charge (c) its inner surface will have same nature charge equal in the magnitude to the charge enclosed (d) its inner surface will have opposite nature but not equal in the magnitude of the charge enclosed

In a region, electric field varies as \(E=2 x^{2}-4\) where \(x\) is distance in S.I. from origin along \(x\) -axis. A positive charge of \(1 \mu \mathrm{C}\) is released with minimum velocity from infinity for crossing the origin, then: (a) the kinetic energy at the origin must be zero (b) the kinetic energy at the origin may be zero (c) the kinetic energy at \(x=\sqrt{2} \mathrm{~m}\) must be zero (d) the kinetic energy at \(x=2 \mathrm{~m}\) mav be zero

Three charged particles are collinear and are in equilibrium. Then: (a) all the charged particles have the same polarity (b) the equilibrium is unstable(c) all the charged particles cannot have the same polarity (d) both (b) and (c) are correct

A point charge \(q\) and a charge \((-q)\) are placed at \(x=-a\) and \(x=+a\) respectively. Which of the following represents a part of \(E-x\) graph ?

A non-conducting solid sphere of radius \(R\) is uniformly charged. The magnitude of electric field due to the sphere at a distance \(r\) from its centre: (a) increases as \(r\) increases for \(r

A conducting solid sphere of radius \(R\) is uniformly charged. The magnitude of the electric field due to the sphere at a distance \(r\) from its centre (a) increases as \(r\) increases (b) decreases as \(r\) increases (c) decreases as \(r\) increases, for \(R

Calculate the work done in carrying a charge \(q\) once round over a closed circular path of radius ' \(r^{\prime}\) and a charge \(Q\) is at the centre : (a) \(\frac{q Q}{4 \pi \varepsilon_{0} r}\) (b) \(\frac{q Q}{4 \pi \varepsilon_{0} \pi r}\) (c) \(\frac{q Q}{4 \pi \varepsilon_{1}}\left(\frac{1}{2 \pi r}\right)\) (d) zero

A point charge \(Q\) is placed at the centre of a circular wire of radius \(R\) having charge \(q\). The force of (a) \(\frac{q Q}{4 \pi \varepsilon_{0} R^{2}}\) point charge and the wire is : electrostatic interaction between (b) zero (c) \(\frac{q^{2}}{4 \pi \varepsilon_{0} R}\) (d) none of these

A point mass \(m\) and charge \(q\) is connected with massless spring of natural length \(L\). Initially spring is in its natural length. If a horizontal uniform electric field \(E\) is switched on (shown in figure), the maximum separation between the point mass and the wall is : (Assume all surfaces are frictionless). (a) \(L+\frac{2 q E}{k}\) (b) \(L+\frac{q E}{k}\) (c) \(L\) (d) none of these

A point charge is projected along the axis of circular ring of charge \(Q\) and radius \(10 \sqrt{2} \mathrm{~cm}\). The distance of the point charge from centre of ring, where acceleration of charged particle is maximum, will be : (a) \(10 \mathrm{~cm}\) (b) \(20 \mathrm{~cm}\) (c) at infinity (d) none of these

If a charged particle is projected on a rough horizontal surface with speed \(v_{0}\), the value of dynamic coefficient of friction if the kinetic energy of system is constant, is: (a) \(\frac{q E}{m g}\) (b) \(\frac{q E}{m}\) (c) \(\underline{q}\) (d) none of these \(g\)

Two charges of values \(2 \mu \mathrm{C}\) and \(-50 \mu \mathrm{C}\) are placed at a distance \(80 \mathrm{~cm}\) apart. The distance of the point from the smaller charge where the intensity will be zero, is : (a) \(20 \mathrm{~cm}\) (b) \(35 \mathrm{~cm}\) (c) \(30 \mathrm{~cm}\) (d) \(25 \mathrm{~cm}\)

Two charged particles of charge \(+2 q\) and \(+q\) have masses \(m\) and \(2 m\) respectively. They are kept in uniform electric field and allowed to move for the same time. The ratio of their kinetic energies is: (a) \(1: 8\) (b) \(16: 1\) (c) \(2: 1\) (d) \(3: 1\)

A copper ball of density \(\rho_{c}\) and diameter \(d\) is immersed in oil of density \(\rho_{\theta}\). What charge should be present on the ball, so that it could be suspended in the oil, if a homogeneous electric field \(E\) is applied vertically upward? (a) \(Q=\frac{\pi d^{2}\left(\rho_{c}-\rho_{0}\right) g}{6 E}\) (b) \(Q=\frac{\pi d^{\vec{j}}\left(\rho_{c}-\rho_{a}\right) g}{6 E}\) (c) \(Q=\frac{\pi d^{3}\left(\rho_{c}-\rho_{0}\right) g}{E}\) (d) None of these

An oil drop of charge of 2 electrons fall freely with a terminal speed. The mass of oil drop so, it can move upward with same terminal speed, if electric field of \(2 \times 10^{3} \mathrm{~V} / \mathrm{m}\) is applied, is : (a) \(3.0 \times 10^{-17} \mathrm{~kg}\) (b) \(3.2 \times 10^{-17} \mathrm{~kg}\) (c) \(2.5 \times 10^{-17} \mathrm{~kg}\) (d) \(3.3 \times 10^{-17} \mathrm{~kg}\)

An electron of mass \(m\) and charge \(e\) leaves the lower plate of a parallel plate capacitor of length \(L\), with an initial velocity \(v_{0}\) making an angle \(\alpha\) with the plate and comeout of the capacitor making an angle \(\beta\) to the plate. The electric field intensity between the plates: (a) \(E:=\frac{m v_{0}^{2} \cos ^{2} \alpha}{e L}(\tan \alpha+\tan \beta)\) (b) \(E=\frac{m v_{0}^{2} \cos ^{2} \alpha}{c L}(\tan \alpha-\tan \beta)\) (c) \(E=\frac{m v_{0}^{7} \cos ^{2} \alpha}{e L}(\tan \beta-\tan \alpha)\) (d) none of the above

An electron is projected with velocity \(10^{7} \mathrm{~m} / \mathrm{s}\) at an angle \(\theta\left(=30^{\circ}\right)\) with horizontal in a region of uniform electric field of \(5000 \mathrm{~N} / \mathrm{C}\) vertically upwards. The maximum distance covered by an electron in vertical direction above its initial level is : (a) \(14.2 \mathrm{~mm}\) (b) \(15 \mathrm{~mm}\) (c) \(12.6 \mathrm{~mm}\) (d) \(14.2 \mathrm{~cm}\)

A pendulum bob of mass ' \(m^{\prime}\) and charge ' \(q^{\prime}\) is suspended by a thread of length \(l\). The pendulum is placed in a region of a uniform electric field \(E\) directed vertically upward. If the electrostatic force acting on the sphere is less than that of gravitational force, the period with which the pendulum oscillates is : (Assume small oscillation) (a) \(T=2 \pi \sqrt{\frac{1}{g+\frac{q E}{m}}}\) (b) \(T=2 \pi \sqrt{\frac{1}{g-\frac{q E}{m}}}\) (c) \(T:=\pi \sqrt{\frac{1}{g-\frac{q E}{m}}}\) (d) \(T=\pi \sqrt{\frac{1}{g+\frac{q E}{m}}}\)

Identical charges of magnitude \(Q\) are placed at \((n-1)\) corners of a regular polygon of \(n\) sides each corner of the polygon is at a distance \(r\) from the centre. The field at the centre is: (a) \(\frac{k Q}{r^{2}}\) (b) \((n-1) \frac{k Q}{r^{2}}\) (c) \(\frac{n}{(n-1)} \cdot \frac{k Q}{r^{2}}\) (d) \(\frac{(n-1)}{n}: \frac{Q}{r^{2}}\)