Chapter 17

If charge \(q\) is placed at the centre of the line joining two equal charges \(Q\), the system of these charges will be in equilibrium if \(q\) is (a) \(-4 Q\) (b) \(-\frac{Q}{4}\) (c) \(-\frac{Q}{2}\) (d) \(+\frac{Q}{2}\)

The maximum field intensity on the axis of a uniformly charged ring of charge \(q\) and radius \(R\) will be (a) \(\frac{1}{4 \pi \varepsilon_{0}} \cdot \frac{q}{3 \sqrt{3} R^{2}}\) (b) \(\frac{1}{4 \pi \varepsilon_{0}} \cdot \frac{2 q}{3 R^{2}}\) (c) \(\frac{1}{4 \pi E_{0}} \cdot \frac{2 q}{3 \sqrt{3} R^{2}}\) (d) \(\frac{1}{4 \pi \varepsilon_{0}} \cdot \frac{3 q}{2 \sqrt{3} R^{2}}\)

Two point charges repel each other with a force of \(100 \mathrm{~N}\). One of the charges is increased by \(10 \%\) and other is reduced by \(10 \%\). The new force of repulsion at the same distance would be (a) \(100 \mathrm{~N}\) (b) \(121 \mathrm{~N}\) (c) \(99 \mathrm{~N}\) (d) None of these

Charges \(2 q,-q\) and \(-q\) lie at the vertices of an equilateral triangle. The value of \(E\) and \(V\) at the centroid of the triangle will be (a) \(E \neq 0\) and \(V \neq 0\) (b) \(E=0\) and \(V=0\) (c) \(E \neq 0\) and \(V=0\) (d) \(E=0\) and \(V \neq 0\)

A point charge \(q\) produces an electric field of magnitude \(2 \mathrm{NC}^{-1}\) at a point distance \(0.25 \mathrm{~m}\) from it. What is the value of charge? (a) \(139 \times 10^{-11} \mathrm{C}\) (b) \(139 \times 10^{11} \mathrm{C}\) (c) \(13.9 \times 10^{-11} \mathrm{C}\) (d) \(1.39 \times 10^{11} \mathrm{C}\)

Equal charges \(q\) each are placed at the vertices \(A\) and \(B\) of an equilateral triangle \(A B C\) of side \(a\). The magnitude of electric field intensity at the point \(C\) is (a) \(\frac{q}{4 \pi \varepsilon_{0} a^{2}}\) (b) \(\frac{\sqrt{2 q}}{4 \pi \varepsilon_{0} a^{2}}\) (c) \(\frac{q \sqrt{3}}{4 \pi \varepsilon_{0} a^{2}}\) (d) \(\frac{2 q}{4 \pi \varepsilon_{0} a^{2}}\)

A hollow metallic sphere of radius \(10 \mathrm{~cm}\) is given a charge of \(3.2 \times 10^{-9} \mathrm{C}\). The electric intensity at a point \(4 \mathrm{~cm}\) from the centre is (a) \(9 \times 10^{-9} \mathrm{NC}^{-1}\) (b) \(288 \mathrm{NC}^{-1}\) (c) \(2.88 \mathrm{NC}^{-1}\) (d) zero

Six charges, three positive and three negative of equal magnitude are to be placed at the vertices of a regular hexagon such that the electric field at \(O\) is double the electric field when only one positive charge of same magnitude is placed at \(R\). Which of the following arrangements of charges is possible for \(P, Q\), \(R, S, T\) and \(U\), respectively? (a) \(+,-,+,-,-,+\) (b) \(+,-,+-,+\) (c) \(+,+,-,+,-\), (d) \(-,+,+,-,+,-\)

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 (a) \(\frac{E^{2} q^{2} t^{2}}{2 m}\) (b) \(\frac{2 E^{2} t^{2}}{q m}\) (c) \(\frac{\mathrm{Eqm}}{2 t}\) (d) \(\frac{E q^{2} m}{2 t^{2}}\)

Work done in carrying a charge \(Q_{1}\) once round a circle of radius \(R\) with a charge \(Q_{2}\) at the centre is (a) \(\frac{Q_{1} Q_{2}}{4 \pi \varepsilon_{0} R^{2}}\) (b) zero (c) \(\frac{Q_{1} Q_{2}}{4 \pi \varepsilon_{0} R}\) (d) infinite

There are two charged identical metal spheres \(A\) and \(B\) repel each other with a force \(3 \times 10^{-5} \mathrm{~N}\). Another identical uncharged sphere \(C\) is touched with \(A\) and then placed at the mid-point between \(A\) and \(B\). Net force on \(C\) is (a) \(1 \times 10^{-5} \mathrm{~N}\) (b) \(2 \times 10^{-5} \mathrm{~N}\) (c) \(1.5 \times 10^{-5} \mathrm{~N}\) (d) \(3 \times 10^{-5} \mathrm{~N}\)

A hollow charged metal sphere has radius \(r\). If the potential difference between its surface and a point at a distance \(3 r\) from the centre is \(V\), then electric field intensity at a distance \(3 r\) is (a) \(\frac{v}{2 r}\) (b) \(\frac{v}{3 r}\) (c) \(\frac{V}{6 r}\) (d) \(\frac{V}{4 r}\)

Two small conducting sphere of equal radius have charges \(+10 \mu \mathrm{C}\) and \(-20 \mu \mathrm{C}\) respectively and placed at a distance \(R\) from each other experience force \(F_{1}\). If they are brought in contact and separated to the same distance,they experience force \(F_{2}\). The ratio of \(F_{1}\) to \(F_{2}\) is (a) \(1: 2\) (b) \(-8: 1\) (c) \(1: 8\) (d) \(-2: 1\)

The electric strength of air is \(2 \times 10^{7} \mathrm{NC}^{-1}\). The maximum charge that a metaleic sphere of diameter \(6 \mathrm{~mm}\) can hold is (a) \(3 \mathrm{nC}\) (b) \(20 \mathrm{nC}\) (c) \(1.5 \mathrm{nC}\) (d) \(2 \mathrm{nC}\)

If the electric flux entering and leaving an enclosed surface are \(\phi_{1}\) and \(\phi_{2}\) respectively, then charge enclosed in closed surface is (a) \(\frac{\phi_{2}-\phi_{1}}{\varepsilon_{0}}\) (b) \(\frac{\phi_{1}+\phi_{2}}{\varepsilon_{0}}\) (c) \(\frac{\phi_{1}-\phi_{2}}{\varepsilon_{0}}\) (d) \(\varepsilon_{0}\left(\phi_{2}-\phi_{1}\right)\)

Two point charges \(+q\) and \(-q\) are held fixed at \((-d, 0)\) and \((d, 0)\) respectively of a \((x, y)\) coordinate system, then (a) the electric field \(\mathrm{E}\) at all points on the \(x\)-axis has the same direction (b) \(\mathrm{E}\) at all points on the \(y\)-axis is along \(\hat{i}\) (c) work has to be done in bringing a test charge from infinity to the origin (d) the dipole moment is 2 qd directed along \(\hat{i}\)

A point charge \(+q\) is placed at a distance \(d\) from an isolated conducting plane. The field at a point \(P\) on the other side of the plane is \(\quad\) [NCERT Exemplar] (a) directed perpendicular to the plane and away from the plane (b) directed perpendicular to the plane but towards the plane (c) directed radially away from the point charge (d) directed radially towards the point charge

In infinite parallel plane sheet of a metal is charged to charge density o coulomb per square metre in a medium of dielectric constant \(K\). Intensity of electric field near the metallic surface will be (a) \(E=\frac{\sigma}{\varepsilon_{0} K}\) (b) \(E=\frac{K}{3 \varepsilon_{0}}\) (c) \(E=\frac{\sigma}{2 \varepsilon_{0} K}\) (d) \(E=\frac{K}{2 \varepsilon_{0}}\)

The magnitude of electric field \(\mathbf{E}\) in the annual region of a charged cylindrical capacitor (a) is same throughout (b) is higher near the outer cylinder than near the inner cylinder (c) varies as \(-\), where \(r\) is the distance from the axis (d) varies as \(\frac{1}{2^{2}}\), where \(r\) is the distance from the axis

A semi-circular arc of radius \(a\) is charged uniformly and the charge per unit length is \(\lambda\). The electric field at its centre is (a) \(\frac{\lambda}{2 \pi \varepsilon_{0}^{a^{2}}}\) (b) \(\frac{\lambda}{4 \varepsilon_{0} a}\) (c) \(\frac{\lambda^{2}}{4 \pi \varepsilon_{0} a}\) (d) \(\frac{\lambda}{2 \pi \varepsilon_{0} a}\)

A positive point charge \(q\) is carried from a point \(B\) to a point \(A\) in the electric field of a point charge \(+Q\) at \(O\). If the permittivity of free space is \(\varepsilon_{0}\), the work done in the process is given by (where, \(a=O A\) and \(b=O R\) ) (a) \(\frac{q Q}{4 \pi \varepsilon_{0}}\left(\frac{1}{a}+\frac{1}{b}\right)\) (b) \(\frac{q Q}{4 \pi \varepsilon_{0}}\left(\frac{1}{a}-\frac{1}{b}\right)\) (c) \(\frac{q Q}{4 \pi \varepsilon_{0}}\left(\frac{1}{a^{2}}-\frac{1}{b^{2}}\right)\) (d) \(\frac{q Q}{4 \pi \varepsilon_{0}}\left(\frac{1}{a^{2}}+\frac{1}{b^{2}}\right)\)

Three charges each of \(+1 \mu \mathrm{C}\) are placed at the corners of an equilateral triangle. If the force between any two charges be \(F\), then the net force on either charge will be (a) \(\sqrt{2} F\) (b) \(F \sqrt{3}\) (c) \(2 F\) (d) \(3 \underline{F}\)

A point \(Q\) lies on the perpendicular bisector of an electrical dipole of dipole moment \(p\). If the distance of \(Q\) from the dipole is \(r\) (much larger than the size of the dipole), then the electric field intensity \(E\) at \(Q\) is proportional to (a) \(r^{-2}\) (b) \(r^{-4}\) (c) \(r^{-1}\) \((d) r^{-3}\)

Charge \(q_{1}=+6.0 \mathrm{nC}\) is on \(Y\)-axis at \(y=+3 \mathrm{~cm}\) and charge \(q_{2}=-6.0 \mathrm{nC}\) is on \(Y\)-axis at \(y=-3 \mathrm{~cm}\). Calculate force on a test charge \(q_{0}=2 \mathrm{nC}\) placed on \(X\)-axis at \(x=4 \mathrm{~cm}\). (a) \(-518 \hat{\mathrm{j}} \mu \mathrm{N}\) (b) \(+51.8 \hat{\mathrm{j}} \mu \mathrm{N}\) (c) \(-5.18 \hat{\mathrm{j}} \mu \mathrm{N}\) (d) \(5.18 \hat{\mathrm{j}} \mu \mathrm{N}\)

Three concentric conducting spherical shells carry charges as follows : \(+Q\) on the inner shell, \(-2 Q\) on the middle shell and \(-5 Q\) on the outer shell. The charge on the inner surface of the outer shell is (a) zero (b) \(+Q\) (c) \(-2 Q\) (d) \(-3 Q\)

An electric dipole consists of two opposite charges, each of magnitude \(1.0 \mu \mathrm{C}\) separated by a distance of \(2.0 \mathrm{~cm}\). The dipole is placed in an external electric field of \(10^{5} \mathrm{NC}^{-1}\). The maximum torque on the dipole is (a) \(0.2 \times 10^{-3} \mathrm{~N}-\mathrm{m}\) (b) \(1 \times 10^{-3} \mathrm{~N}-\mathrm{m}\) (c) \(2 \times 10^{-3} \mathrm{~N}-\mathrm{m}\) (d) \(4 \times 10^{-3} \mathrm{~N}-\mathrm{m}\)

A charged body has an electric flux \(\phi\) associated with it. The body is now placed inside a metallic container. The electric flux, \(\phi_{1}\) associated with the container will be (a) \(\phi_{1}=0\) (b) \(0<\phi_{1}<\phi\) (c) \(\phi_{1}=\phi\) (d) \(\phi_{1}>\phi\)

The electric field in the space between the plates of a discharge tube is \(3.25 \times 10^{-4} \mathrm{NC}^{-1}\). If mass of proton is \(1.67 \times 10^{-27} \mathrm{~kg}\) and its charge is \(1.6 \times 10^{-19} \mathrm{C}\), the force often the proton in the field is (a) \(10.4 \times 10^{-15} \mathrm{~N}\) (b) \(20 \times 10^{-23} \mathrm{~N}\) (c) \(5.40 \times 10^{-15} \mathrm{~N}\) (d) \(5.20 \times 10^{-15} \mathrm{~N}\)

A charged body has an electric flux \(\phi\) associated with it. The body is now placed inside a metallic container. The electric flux, \(\phi_{1}\) associated with the container will be (a) \(\phi_{1}=0\) (b) \(0<\phi_{1}<\phi\) (c) \(\phi_{1}=\phi\) (d) \(\phi_{1} \geq \phi\)

The dimensional forumula of absolute permittivity of air or free space \(\left(\varepsilon_{0}\right)\) is (a) \(\left[\mathrm{M}^{-1} \mathrm{~L}^{-3} \mathrm{~T}^{4} \mathrm{~A}^{2}\right]\) (b) \(\left[\mathrm{M}^{\mathrm{D}} \mathrm{L}^{-3} \mathrm{~T}^{3} \mathrm{~A}^{3}\right]\) (c) \(\left[\mathrm{M}^{-1} \mathrm{~L}^{-3} \mathrm{~T}^{-3} \mathrm{~A}\right]\) (d) \(\left[\mathrm{M}^{-1} \mathrm{~L}^{-3} \mathrm{TA}^{2}\right]\)

Two point charges \(+3 \mu \mathrm{C}\) and \(+8 \mu \mathrm{C}\) repel each other with a force of \(40 \mathrm{~N}\). If a charge of \(-5 \mu \mathrm{C}\) is added to each of them, then the force between them will become (a) \(-10 \mathrm{~N}\) (b) \(+10 \mathrm{~N}\) (c) \(+20 \mathrm{~N}\) (d) \(-20 \mathrm{~N}\)

Two spheres of radii \(R_{1}\) and \(R_{2}\) joined by a fine wire are raised to a potential \(V\). Let the surface charge densities at these two spheres be \(\sigma_{1}\) and \(\sigma_{2}\), respectively. Then the ratio \(\frac{\sigma_{2}}{\sigma_{1}}\) has a value (a) \(\frac{R_{\mathrm{f}}}{R_{2}}\) (b) \(\frac{R_{2}}{R_{1}}\) (c) 1 (d) \(\left(\frac{R_{2}}{R_{1}}\right)^{2}\)

A polythene piece, rubbed with wool, is found to have negative charge of \(4 \times 10^{-7}\) C. The number of electrons transferred from wool to polythene is (a) \(1.5 \times 10^{12}\) (b) \(2.5 \times 10^{12}\) (c) \(2.5 \times 10^{13}\) (d) \(3.5 \times 10^{13}\)

A non-conducting ring of radius \(0.5 \mathrm{~m}\) carries total charge of \(1.11 \times 10^{-10}\) C distributed non-uniformly on its circumference producting an electric field everywhere in space. The value of the line integral \(\oint_{l=\infty}^{l=0}-E \cdot d l(l=0\), being centre of ring) in volt is (a) \(+2\) (b) \(-1\) (c) \(-2\) (d) zero

An electron of mass \(M_{e}\), initially at rest, moves through a certain distance in a uniform electric field in time \(t_{1}\). A proton of mass \(M_{p}\) also initially at rest, takes time \(t_{2}\) to move through an equal distance in this uniform electric field. Neglecting the effect of gravity, the ratio \(t_{2} / t_{1}\) is nearly equal to (a) 1 (b) \(\sqrt{M_{p} / M_{e}}\) (c) \(\sqrt{M_{e} / M_{p}}\) (d) 1836

A solid conducting sphere having a charge \(Q\) is surrounded by an uncharged concentric conducting hollow spherical shell. Let the potential difference between the surface of the solid sphere and that of the outer surface of the hollow shell be \(V\). If the shell is now given a charge \(-3 Q\), the new potential difference between the same two surfaces is (a) \(\underline{V}\) (b) \(2 \mathrm{~V}\) (c) \(4 V\) (d) \(-2 V\)

A charged spherical conductor of radius \(R\) carries a charge \(q_{0} .\) A point test charge \(q_{0}\) is placed at a distance \(x\) from the surface of the conductor. The force experienced by the test charge will be proportional to (a) \((R+x)^{2}\) (b) \((R-x)^{2}\) (c) \(\frac{1}{(R-x)^{2}}\) (d) \(\frac{1}{(R+x)^{2}}\)

A slab of copper of thickness, \(b\) is inserted in between the plates of parallel plate capacitor as shown in figure. The separation between the plates is \(d\) if \(b=d / 2\), then the ratio of capacities of capacitors after and before inserting the slab will be (a) \(\sqrt{2}: 1\) (b) \(2: 1\) (c) \(1: 1\) (d) \(1: \sqrt{2}\)

An insulated sphere of radius \(R\) has charge density \(\rho .\) The electric field at a distance \(r\) from the centre of the sphere \((r

A spherical charged conductor has \(\sigma\) as the surface density of charge. The electric field on its surface is \(E\). If the radius of the sphere is doubled, keeping the surface density of the charge unchanged, what will be the electric field on the surface of the new sphere? (a) \(\frac{E}{4}\) (b) \(\frac{E}{2}\) (c) \(E\) (d) \(2 \bar{E}\)

Two identical metal plates are given positive charges \(Q_{1}\) and \(Q_{2}\left(

Two identical capacitors have the same capacitance C. One of them is charged to potential \(V_{1}\) and the other to \(V_{2}\). The negative ends of the capacitors are connected together. When the positive ends are also connected, the decrease in energy of the system is (a) \(\frac{1}{4} C\left(V_{1}^{2}-V_{2}^{2}\right)\) (b) \(\frac{1}{4} C\left(V_{1}^{2}+V_{2}^{2}\right)\) (c) \(\frac{1}{4} C\left(V_{1}-V_{2}\right)^{2}\) (d) \(\frac{1}{4} C\left(V_{1}+V_{2}\right)^{2}\)

A given charge situated at a certain distance from an electric dipole in the end on position, experiences a force \(F\). If the distance of charge is doubled, the force acting on the charge will be (a) \(2 \mathrm{~F}\) (b) \(F / 2\) (c) \(F / 4\) (d) \(F / 8\)

Two point charges of \(1 \mu \mathrm{C}\) and \(-1 \mu \mathrm{C}\) are separated by a distance of \(100 \mathrm{~A}\). A point \(P\) is at a distance of \(10 \mathrm{~cm}\) from the mid-point and on the perpendicular bisector of the line joining the two charges. The electric field at \(P\) will be (a) \(9 \mathrm{NC}^{-1}\) (b) \(0.9 \mathrm{Vm}^{-1}\) (c) \(90 \mathrm{Vm}^{-1}\) (d) \(0.09 \mathrm{NC}^{-1}\)

The distance between two point charges is increased by \(10 \%\). The force of interaction between them (a) increased by \(109_{6}\) (b) decreased by \(10 \%\) (c) decreased by \(179 \%\) (d) decreased by \(21 \%\)

Two point charges exert on each other a force \(F\) when they are placed \(r\) distance apart in air. If they are placed \(R\) distance apart in a medium of dielectric constant \(K\), they exert the same force. The distance \(R\) equals (a) \(\frac{r}{K}\) (b) \(r \bar{K}\) (c) \(r \sqrt{K}\) (d) \(\frac{r}{\sqrt{K}}\)

Two point charges of \(+2 \mu \mathrm{C}\) and \(+6 \mu \mathrm{C}\) repel each other with a force of \(12 \mathrm{~N}\). If each of is given an additional charge of \(-4 \mu \mathrm{C}\). What will be the new force? (a) \(-6 \mathrm{~N}\) (b) 0 (c) \(-2 \mathrm{~N}\) (d) \(-4 \mathrm{~N}\)

Two spherical conductors \(A\) and \(B\) of radii \(1 \mathrm{~mm}\) and \(2 \mathrm{~mm}\) are separated by a distance of \(5 \mathrm{~cm}\) and are uniformly charged. If the spheres are connected by a conducting wire, then in equilibrium condition, the ratio of the magnitude of the electric fields at the surfaces of spheres \(A\) and \(B\) is (a) \(4: 1\) (b) \(1: 2\) (c) \(2: 1\) (d) \(1: 4\)

A neutral water molecule \(\left(\mathrm{H}_{2} \mathrm{O}\right)\) in its vapour state has an electric dipole moment of \(6 \times 10^{-30} \mathrm{Cm}\). If the molecule is placed in an electric field of \(1.5 \times 10^{4} \mathrm{NC}^{-1}\), the maximum torque that the field can exert on it is nearly (a) \(4.5 \times 10^{-26} \mathrm{~N}-\mathrm{m}\) (b) \(4 \times 10^{-34} \mathrm{~N}-\mathrm{m}\) (c) \(9 \times 10^{-26} \mathrm{~N}-\mathrm{m}\) (d) \(6 \times 10^{-26} \mathrm{~N}-\mathrm{m}\)

If \(E_{a}\) be the electric field strength of a short dipole at a point on its axial line and \(E_{e}\) that on equatorial line at the same distance, then (a) \(E_{c}=2 E_{a}\) (b) \(E_{a}=2 E_{e}\) (c) \(E_{a}=E_{c}\) (d) None of these