Chapter 17

A \(10 \mu \mathrm{F}\) capacitor and a \(20 \mu \mathrm{F}\) capacitor are connected in series across \(200 \mathrm{~V}\) supply line. The charged capacitors are then disconnected from the line and reconnected with their positive plates together and negative plates together and no external voltage is applied. What is the potential difference across each capacitor? (a) \(\frac{800}{9} \mathrm{~V}\) (b) \(\frac{800}{3} \mathrm{~V}\) (c) \(400 \mathrm{~V}\) (d) \(200 \mathrm{~V}\)

A charge \((-q)\) and another charge \((+Q)\) are kept a two points \(A\) and \(B\), respectively. Keeping the charg \((+Q)\) fixed at \(B\), the charge \((-q)\) at \(A\) is moved \(t\) another point \(C\) such that \(A B C\) forms an equilatera triangle of side \(l\). The net work done in moving th charge \((-q)\) is (a) \(\frac{1}{4 \pi \varepsilon_{0}} \frac{Q q}{l}\) (b) \(\frac{1}{4 \pi \varepsilon_{0}} \frac{Q q}{l^{2}}\) (c) \(\frac{1}{4 \pi \varepsilon_{0}} Q q l\) (d) zero

A parallel plate capacitor is made by stocking \(n\) equally spaced plates connected alternately. If, the capacitance between any two plates is \(x\), then the total capacitance is, (a) \(n x\) (b) \(n / x\) (c) \(n x^{2}\) (d) \((n-1) x\)

The flux entering and leaving a closed surface are \(5 \times 10^{5}\) and \(4 \times 10^{5}\) in MKS unit respectively, then the charge inside the surface will be (a) \(-886 \times 10^{-7} \mathrm{C}\) (b) \(7.86 \times 10^{-7} \mathrm{C}\) (c) \(6.85 \times 10^{7} \mathrm{C}\) (d) \(6.85 \times 10^{-7} \mathrm{C}\)

Six identical capacitors are joined in parallel, charged to a potential difference of \(10 \mathrm{~V}\), separated and then connected in series, i.e., the positive plate of one is connected to negative plate of other. Then potential difference between free plates is (a) \(10 \mathrm{~V}\) (b) \(30 \mathrm{~V}\) (c) \(60 \mathrm{~V}\) (d) \(\frac{10}{6} \mathrm{~V}\)

The potential difference applied to an X-ray tube is \(5 \mathrm{kV}\) and current through it is \(3.2 \mathrm{~mA}\). Then, the number of electrons striking the target per second is (a) \(2 \times 10^{10}\) (b) \(3 \times 10^{18}\) (c) \(2 \times 10^{16}\) (d) \(5 \times 10^{15}\)

\(\oint \mathbf{E} \cdot d \mathbf{S}=0\) over a surface, then \(\quad\) [NCERT Exemplar] (a) the electric field inside the surface and on it is zero (b) the electric field inside the surface is necessarily uniform (c) the number of flux lines entering the surface must be equal to the number of lux lines leaving it (d) all charges must necessarily be outside the surface

Equipotentials at a great distance from a collection of charges whose total sum is not zero are approximately. \(\quad\) [NCERT Exemplar] (a) spheres (b) planes (c) paraboloids (d) ellipsoids

A positive charge \(Q\) is located at the centre of a thin metallic spherical shell. Select the correct statement(s) from the following. (a) The electric field at any point outside the shell is zero (b) The electrostatic potential at any point outside the shell is \(\frac{Q}{4 \pi \varepsilon_{0} r}\), where, \(r\) is the distance of the point from centre (c) The outer surface of the spherical shell is an equipotential surface (d) The electric field at any point inside the shell, other than centre point is, zero

A circular ring of radius \(R\) with uniformly distributed charge \(q\) is placed in their \(y z\)-plane with its centre at the origin. Select the correct statement(s) out of the following. (a) The electric intensity is maximum at \(x=\pm \sqrt{2} R\) (b) The electric intensity is maximum at \(x=\pm \frac{\sqrt{2}}{2} R\) (c) The maximum intensity has a magnitude \(\frac{q}{6 \sqrt{3} \pi \varepsilon_{0} R^{2}}\) (d) The maximum intensity is \(\frac{q}{6 \sqrt{6} \pi \varepsilon_{0} R^{2}}\)

The electric field at a point is \(\quad\) [NCERT Exemplar] (a) always continuous (b) continuous if there is no charge at that point (c) discontinuous only if there is a negative charge at that point (d) discontinuous if there is a charge at that point

An electric field is given by \(\mathbf{E}=(y \hat{\mathbf{i}}+x \hat{\mathbf{j}}) \mathrm{NC}^{-1}\). The work done in moving a \(1 \mathrm{C}\) charge from \(\mathbf{r}_{A}=(2 \hat{\mathbf{i}}+2 \hat{\mathbf{j}})\) \(\mathrm{m}\) to \(\mathbf{r}_{B}=(4 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}) \mathrm{m}\) is (a) \(2 y\) (b) \(3 y\) (c) zero (d) infinity

A parallel plate capacitor of plate area \(A\) and plate separation \(d\) is charged to potential difference \(V\) and then the battery is disconnected. A slab of dielectric constant \(K\) is then inserted between the plates of the capacitor so as to fill the space between the plates. If \(Q, E\) and \(W\) denotes respectively the magnitude of charges on each plate, the electric field between the plates (after the slab is inserted) and work done on the system, in the process of inserting the slab, then (a) \(Q=\frac{\varepsilon_{0} A V}{d}\) (b) \(Q=\frac{\varepsilon_{0} K A V}{d}\) (c) \(E=\frac{V}{K d}\) (d) \(W=\frac{\varepsilon_{0} A V^{2}}{2 d}\left[1-\frac{1}{K}\right]\)

If there were only one type of charge in the universe, then [NCERT Exemplar] (a) \(\oint \mathrm{E} \cdot d \mathrm{~s} \neq 0\) on any surface (b) \(\oint \mathrm{E} \cdot d \mathrm{~S}=0\) if the charge is outside the surface (c) \(\oint \mathrm{E} \cdot d \mathbf{S}\) could not be defined (d) \(\oint \mathrm{E} \cdot d \mathrm{~S}=\frac{q}{\varepsilon_{0}}\) if charges of magnitude \(q\) where inside the surface

A parallel plate capacitor is connected to a battery. A metal sheet of negligible thickness is placed between the plates at their centre. Which of the following is correct? (a) Equal and opposite charges will appear in the low these faces of metal sheet (b) Capacity remain same (c) Potential difference between the plates increases (d) Battery supplies more charge

A sphere of radius \(r\) is charged to a potential \(V\). The outward pull per unit area of its surface is given by (a) \(\frac{4 \pi \varepsilon_{0} V^{2}}{r^{2}}\) (b) \(\frac{\varepsilon_{0} V^{2}}{2 r^{2}}\) (c) \(\frac{2 \pi \varepsilon_{0} V^{2}}{r^{2}}\) (d) \(\frac{\varepsilon_{0} V^{2}}{4 r^{2}}\)

Consider a region inside which there are various types of charges but the total charge is zero. At points outside the region (a) the electric field is necessarily zero (b) the electric field is due to the dipole moment of the charge distribution only (c) the dominant electric field is \(\propto \frac{1}{r^{3}}\), for large \(r\), where \(r\) is the distance from a origin in this region (d) the work done to move a charged particle along a closed path, away from the region, will be zero

\(n\) small drops of same size are charged to \(V\) volt each. If they coalesce to form a single large drop, then its potential will be (a) \(\mathrm{Vn}\) (b) \(\mathrm{Vn}^{-1}\) (c) \(V n^{1 / 3}\) (d) \(V n^{2 \beta}\)

A parallel plate capacitor is charged and the charging battery is then disconnected. If the plates of the capacitor are moved farther apart by means of insulating handles, then which of the following is correct? (a) The charge on the capacitor increases (b) The voltage across the plates increases (c) The capacitance increases (d) The electrostatic energy stored in the capacitor increases

A cube of side \(b\) has a charge \(q\) at each of its vertices. Determine the potential and electric field due to this charge array at the centre of the cube. [NCERT] (a) \(\frac{4 q}{\sqrt{3} \pi \varepsilon_{0} b}\) (b) \(\frac{3 q}{\sqrt{2} \pi \varepsilon_{0} b}\) (c) \(\frac{3 q}{\sqrt{2} \pi \varepsilon_{0} b^{2}}\) (d) \(\frac{2 q}{\sqrt{3} \pi \varepsilon_{0} b}\)

In a region of space, the electric field is given by \(\mathbf{E}=8 \hat{\mathbf{i}}+` 4 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}\). The electric flux through a surface of area of 100 units \(x y\)-plane is (a) 800 units (b) 300 units (c) 400 units (d) 1500 units

A closed surface \(S\) is constructed around a metal wire connected to a battery and a key, \(K\). On pressing the key, number of free electrons entering per second is equal to number of free electrons leaving per second. The electric flux through the closed surface is (a) decreased (b) increased (c) remains constant (d) remaining zero

In a region of space having a unifrom electric field \(E\), a hemispherical bowl of radius \(r\) is placed. The electric flux \phi through the bowl is (a) \(2 \pi r E\) (b) \(4 \pi r^{2} E\) (c) \(2 \pi r^{2} E\) (d) \(\pi r^{2} E\)

A positive charge \(Q\) is uniformly distributed along a circular ring of radius \(R\). A small test charge \(q\) is placed at the centre of the ring figure. Then [NCERT Exemplar] (a) If \(q>0\) and is displaced away from the centre in the plane of the ring, it will be pushed back towards the centre (b) If \(q<0\) and is displaced away from the centre in the plane of the ring, it will never return to the centre and will continue moving till it hits the ring (c) \(q<0\), it will perform SHM for small displacement along the axis (d) \(q\) at the centre of the ring is in an unstable equilibrium within the plane of the ring for \(q>0\)

Two free protons are separated by a distance of \(1 \AA\). If one proton is kept at least distance and the other is released, the kinetic energy of second proton when it is at infinite separation is (a) \(23.0 \times 10^{-19} \mathrm{~J}\) (b) \(11.5 \times 10^{-19} \mathrm{~J}\) (c) \(2.3 \times 10^{-19} \mathrm{~J}\) (d) zero

The work done to move a charge along an equipotential from \(A\) to \(B \quad\) NCERT Exemplar] (a) cannot be defined as \(-\int_{A}^{B} \mathrm{E} \cdot d 1\) (b) must be defined as \(-\int_{A}^{B} \mathrm{E} \cdot d 1\) (c) is zero (d) can have a non-zero value

A regular hexagon of side \(10 \mathrm{~cm}\) has a charge \(5 \mu \mathrm{C}\) at each of its vartices. The potential at the centre of the hexagon is? [NCERT] (a) \(3.7 \times 10^{6} \mathrm{~V}\) (b) \(2.7 \times 10^{6} \mathrm{~V}\) (c) \(4 \times 10^{6} \mathrm{~V}\) (d) \(5 \times 10^{7} \mathrm{~V}\)

A positive charged thin metal ring of radius \(R\) is fixed in the \(x y\)-plane with the centre at the origin \(O . \mathrm{A}\) negatively charged particle \(P\) is released from rest at the point \(\left(0,0, z_{0}\right)\) where, \(z_{0}>0 .\) Then, the motion of \(P\) is (a) periodic, for all values of \(z_{0}\) satisfying \(0 \leq z_{0}<\infty\) (b) simple harmonic, for all values of \(z_{0}\) satisfying \(0 \leq z_{0} \leq R\) (c) approximately simple harmonic, provided \(z_{0}

27 identical drops of mercury are charged simultaneously to the same potential of \(10 \mathrm{~V}\) each. Assuming drops to be spherical, if all the charged drops are made to combine to form one larger drop, then the potential of larger drop would be (a) \(45 \mathrm{~V}\) (b) \(135 \mathrm{~V}\) (c) \(270 \mathrm{~V}\) (d) \(90 \mathrm{~V}\)

For a point situated outside the sphere at a \(r>R\), the electric field is given by (a) \(E=\frac{1}{4 \pi \varepsilon_{0}} \cdot \frac{Q}{r^{2}}\) (b) \(E=\frac{1}{4 \pi \varepsilon_{0}} \cdot \frac{-Q}{r^{2}}\) (c) \(E=\frac{1}{4 \pi \varepsilon_{0}} \cdot \frac{Q}{r^{3}}\) (d) \(E=\frac{1}{4 \pi \varepsilon_{0}} \cdot \frac{Q^{2}}{r^{2}}\)

For a point situated inside the sphere at a distance \(r\) from its centre i.e., \(r

A capacitor connected to a \(10 \mathrm{~V}\) battery collects a charge of \(40 \mu \mathrm{C}\) with air as dielectric and \(100 \mu \mathrm{C}\) with a given oil as dielectric. The dielectric constant of the oil is (a) \(1.5\) (b) \(2.0\) (c) \(2.5\) (d) \(3.0\)

If radius of sphere be \(0.1 \mathrm{~m}\) and the sphere contains \(1 \mu \mathrm{C}\) charge, then electric field at its surface has a magnitude (a) \(9 \times 10^{11} \mathrm{NC}^{-1}\) (b) \(9 \times 10^{5} \mathrm{NC}^{-1}\) (c) \(3 \times 10^{5} \mathrm{NC}^{-1}\) (d) \(\frac{1}{9} \times 10^{-5} \mathrm{NC}^{-1}\)

The capacitance of a spherical condensers is \(1 \mu \mathrm{F}\). If the spacing between two spheres is \(1 \mathrm{~mm}\), the radius of the outer sphere is (a) \(3 \mathrm{~m}\) (b) \(7 \mathrm{~m}\) (c) \(8 \mathrm{~m}\) (d) \(9 \mathrm{~m}\)

Electric potential and electric potential energy both are (a) scalars (b) vectors (c) both (a) and (b) (d) neither (a) nor (b)

A parallel plate capacitor has a capacitance of \(50 \mu \mathrm{F}\) in air and \(100 \mu \mathrm{F}\) when immersed in an oil. The dielectric constant \(K\) of the oil is (a) \(2.2\) (b) \(1.1\) (c) \(0.45\) (d) \(5.0\)

A parallel plate capacitor is made of two dielectric blocks in series. One of the blocks has thickness \(d_{1}\) and dielectric constant \(K_{1}\) and the other has thickness \(d_{2}\) and dielectric constant \(K_{2}\) as shown in figure. This arrangement can be thought as a dielectric slab of thickness \(d\left(=d_{1}+d_{2}\right)\) and effective dielectric constant \(K .\) The \(K\) is \(\quad\) [NCERT Exemplar] (a) \(\frac{K_{1} d_{1}+K_{2} d_{2}}{d_{1}+d_{2}}\) (b) \(\frac{K_{1} d_{1}+K_{2} d_{2}}{K_{1}+K_{2}}\) (c) \(\frac{K_{1} K_{2}\left(d_{1}+d_{2}\right)}{\left(K_{1} d_{1}+K_{2} d_{2}\right)}\) (d) \(\frac{2 K_{1} K_{2}}{K_{1}+K_{2}}\)

The electric potential at a point due to a given charge varies inversely as the square of the distance of the point from the charge. The statement is (a) true (b) false (c) neither true nor false (d) None of these Passage III The given figure shown an arrangement of four parallel, conducting plate of area \(A\) each. All the plates are equally separated by \(d .\) The plates \(A\) and \(D\) are joined together and a battery of emf \(E\) volt, is attached between the plates \(B\) and \(C\). \(A\)

The force on each plate of parallel plate capacitor has a magnitude equal to \(\frac{1}{2} Q E\), where \(Q\) is the charge on the capacitor and \(E\) is the magnitude of electric field between the plates. Then (a) \(\frac{E}{2}\) contributes to the force against which the plates are moved (b) \(\frac{E}{3}\) contributes to the force against which the plates are moved (c) \(E\) contributes force against which the plates are moved (d) None of the above

An electrical technician requires a capacitance of \(2 \mu \mathrm{F}\) in a circuit across a potential difference of \(1 \mathrm{kV}\). A large number of \(1 \mu \mathrm{F}\) capacitors are available to him each of which can withstand a potential difference of not more than \(400 \mathrm{~V}\). Suggest a possible arrangement that requires the minimum number of capacitors. [NCERT] (a) six rows having 3 capacitors in each row (b) three rows having 6 capacitors in each row (c) nine rows having 2 capacitors in each row (d) Two rows having 9 capacitors in each row

Match the following Column I with Column II. Column 1\. Electrical capacity II. Permittivity of free space III. Electrical potential IV. Electrical energy Column II (A) \(\left[\mathrm{M}^{-} \mathrm{L}^{-3} \mathrm{~T}^{4} \mathrm{~A}^{2}\right]\) (B) \(\left[\mathrm{M}^{\prime} \mathrm{L}^{2} \mathrm{~T}^{-3} \mathrm{~A}^{-1}\right]\) (C) \(\left[\mathrm{M}^{\prime} \mathrm{L}^{2} \mathrm{~T}^{-2}\right]\) (D) \(\left[\mathrm{M}^{-1} \mathrm{~L}^{-3} \mathrm{~T}^{4} \mathrm{~A}^{2}\right]\) (a) \(1-\mathrm{A}, \mathrm{ll}-\mathrm{D}, \mathrm{IIl}-\mathrm{B}, \mathrm{IV}-\mathrm{C}\) (b) \(1-D, 11-A, 111-C\), IV-C (c) \(1-\mathrm{D}, 11-\mathrm{A}, 1 \mathrm{ll}-\mathrm{C}, \mathrm{IV}-\mathrm{B}\) (d) \(1-A, 11-D, 11]-C, T V-B\)

A \(600 \mathrm{pF}\) capacitor is charged by a \(200 \mathrm{~V}\) supply. Then, it is disconnected from the supply and is connected to another uncharged \(600 \mathrm{pF}\) capacitor. How much electrostatic energy is lost in the process? [NCERT] (a) \(4 \times 10^{-6} \mathrm{~J}\) (b) \(6 \times 10^{-6} \mathrm{~J}\) (c) \(5 \times 10^{-6} \mathrm{~J}\) (d) \(8 \times 10^{-6} \mathrm{~J}\)

Match the following Column I with Column II. Column I I. Coulomb force and gravitational force, both fallow II. In series combination of capacitors III. In parallel combination of capacitons IV. Electric dipole Column II (A) charge on each capacitor is same (B) potential difference across each capacitor is same (C) stable equilibrium (D) inverse square law of distance (a) \(1-\mathrm{D}, \|-\mathrm{A}, \mathrm{Ill}-\mathrm{B}, \mathrm{IV}-\mathrm{C}\) (b) \(1-A, 11-B, I \|-C, I V-D\) (c) \(1-\mathrm{B}, \mathrm{ll}-\mathrm{C}, 1 \mathrm{II}-\mathrm{D}, \mathrm{IV}-\mathrm{A}\) (d) \(1-\mathrm{D}, 11-\mathrm{A}, \mathrm{III}-\mathrm{C}, \mathrm{IV}-\mathrm{A}\)

Match the following Column I with Column II. Column L. Dipole moment II. Electric field III. Torque IV. Gauss's theorem Column II (A) \(|\mathrm{E}|=\frac{1}{4 \pi \varepsilon_{0}} \frac{q}{r^{2}}\) (B) \(\tau=\rho E \sin \theta\) (C) \(|\mathbf{p}|=q \times 2 a\) (D) \(\oint_{S} E \cdot d \mathbf{S}=\frac{q}{\varepsilon_{0}}\) (a) \(1-\mathrm{C}, 11-\mathrm{A}, \mathrm{IIl}-\mathrm{B}, \mathrm{TV}-\mathrm{D}\) (b) \(1-\mathrm{A}, 11-\mathrm{B}, 11]-\mathrm{C}, \mathrm{TV}-\mathrm{D}\) (c) \(1-\mathrm{D}, 11-\mathrm{A}, \mathrm{IIl}-\mathrm{C}, \mathrm{TV}-\mathrm{B}\) (d) \(1-D, 11-B, I I]-C, I V-A\)

Assertion-Reason type. Each of these contains two Statements : Statement I (Assertion), Statement II (Reason). Each of these questions also has four alternative choice, only one of which is correct. You have to select the correct choices from the codes (a), (b), (c) and (d) given below (a) If both Assertion and Reason are true and the Reason is correct explanation of the Assertion (b) If both Assertion and Reason are true but Reason is not the correct explanation of the Assertion (c) If Assertion is true but Reason is false (d) If Assertion is false but the Reason is true Assertion Force between two charges decreases, when air separating the charges is replaced by water. Reason Medium intervening between the charges has no effect on force.

Assertion-Reason type. Each of these contains two Statements : Statement I (Assertion), Statement II (Reason). Each of these questions also has four alternative choice, only one of which is correct. You have to select the correct choices from the codes (a), (b), (c) and (d) given below (a) If both Assertion and Reason are true and the Reason is correct explanation of the Assertion (b) If both Assertion and Reason are true but Reason is not the correct explanation of the Assertion (c) If Assertion is true but Reason is false (d) If Assertion is false but the Reason is true Assertion During charging by rubbing, the insulating material with lower work function becomes positively charged. Reason Electrons are negatively charged.

Assertion-Reason type. Each of these contains two Statements : Statement I (Assertion), Statement II (Reason). Each of these questions also has four alternative choice, only one of which is correct. You have to select the correct choices from the codes (a), (b), (c) and (d) given below (a) If both Assertion and Reason are true and the Reason is correct explanation of the Assertion (b) If both Assertion and Reason are true but Reason is not the correct explanation of the Assertion (c) If Assertion is true but Reason is false (d) If Assertion is false but the Reason is true Assertion A point charge is brought an electric field. The field at a nearby point will be increase. Whatever the nature of charge. Reason The electric field is independent of the nature of charge.

Assertion-Reason type. Each of these contains two Statements : Statement I (Assertion), Statement II (Reason). Each of these questions also has four alternative choice, only one of which is correct. You have to select the correct choices from the codes (a), (b), (c) and (d) given below (a) If both Assertion and Reason are true and the Reason is correct explanation of the Assertion (b) If both Assertion and Reason are true but Reason is not the correct explanation of the Assertion (c) If Assertion is true but Reason is false (d) If Assertion is false but the Reason is true Assertion The displacement current goes through the gap between the plates of the capacitor when the charge of the capacitor does not change. Reason The displacement current arises in region in which the electric field and hence the electric flux does not change with time.

Assertion-Reason type. Each of these contains two Statements : Statement I (Assertion), Statement II (Reason). Each of these questions also has four alternative choice, only one of which is correct. You have to select the correct choices from the codes (a), (b), (c) and (d) given below (a) If both Assertion and Reason are true and the Reason is correct explanation of the Assertion (b) If both Assertion and Reason are true but Reason is not the correct explanation of the Assertion (c) If Assertion is true but Reason is false (d) If Assertion is false but the Reason is true Assertion No two electric field lines can intersect one another at any point in space. Reason Electric field lines always start from a positive charge and end on a negative charge.

Assertion-Reason type. Each of these contains two Statements : Statement I (Assertion), Statement II (Reason). Each of these questions also has four alternative choice, only one of which is correct. You have to select the correct choices from the codes (a), (b), (c) and (d) given below (a) If both Assertion and Reason are true and the Reason is correct explanation of the Assertion (b) If both Assertion and Reason are true but Reason is not the correct explanation of the Assertion (c) If Assertion is true but Reason is false (d) If Assertion is false but the Reason is true Assertion Net electric flux over a cube enclosing an electric dipole is zero. Reason Total net charge on an electric dipole is zero.