IISER Physics - Electrostatistics
Exam Duration: 45 Mins Total Questions : 30
Electric potential difference is defined as the
- (a)
Scalar function of position
- (b)
single-valued scalar function of two positions
- (c)
potential energy of a system of charges
- (d)
potential associated with the electric field
A parallel plate capacitor has charge +Q and -Q on its plate.The separation between the plates is doubled
- (a)
charge on the plates is reduced to half
- (b)
capacitance is doubled
- (c)
Potential difference between the plates is doubled
- (d)
Electric field between the plates is reduced to half
How many time constants must elapse before a capacitor in an RC circuit is charged to within 1% of its equilibrium charge?
- (a)
0.868
- (b)
2
- (c)
1.152
- (d)
4.606
Two identical parallel plate capacitors are joined in series to a battery of 100 volts.A dielectric slab of relative permittivity 4 is inserted between the plates of the second capacitor.The potential difference across this second capacitor now will be
- (a)
10 V
- (b)
20 V
- (c)
30 V
- (d)
40 V
An electric diploe with a moment 2 cm and moment of inertia 5 kg.\({ m }^{ 2 }\) about its dipole equator is placed in a uniform electric field \(10V{ m } ^ { -1 }\). For small amplitudes of motion, it executes simple harmonic motion. The restoring force per unit mass per unit displacement( in \(Nk { g } ^ { -1 } { m } { -1 }\)) is
- (a)
1
- (b)
\(2\pi\)
- (c)
\(4\pi\)
- (d)
4
The electric field due to an infinite line of charge at a distance r is proportional to
- (a)
r
- (b)
\({ 1 } / { r }\)
- (c)
\({ 1 } / { r } ^{ 2 }\)
- (d)
log r
Choose INCORRECT statement
- (a)
Charge is quantitised
- (b)
Charge is conserved
- (c)
Nuclear force is charge dependent
- (d)
Fraction of electronic charge may exist
If mass of electron \({ m }_{ e }=9.11\times { 10 }^{ -31 }\)kg and charge on electron,e=\({ m }_{ e }=1.60\times { 10 }^{ -19 }\)C, then the ratio of electrostatic(\({ F } _ { e }\))and gravitational(\({ F } _ { g }\)) forces that act between two stationary electrons is of the order of
- (a)
\({ 10 } ^ { 12 }\)
- (b)
\({ 10 } ^ { 22 }\)
- (c)
\({ 10 } ^ { 32 }\)
- (d)
\({ 10 } ^ { 42 }\)
Figure shows a charge +Q at a distance 2d froma charge -Q and a point P at a distance d from -Q.The field strength at p is
- (a)
\(\frac { Q }{ 4\pi { \epsilon }_{ 0 }{ d }^{ 2 } } \)along BP
- (b)
\(\frac { Q }{ 36\pi { \epsilon }_{ 0 }{ d }^{ 2 } } \)along PA
- (c)
\(\frac { 5Q }{ 18\pi { \epsilon }_{ 0 }{ d }^{ 2 } } \)along BP
- (d)
\(\frac { 2Q }{ 9\pi { \epsilon }_{ 0 }{ d }^{ 2 } } \)along PB
Figure shows a charge +Q at a distance 2d away from a charge -Q and a point P at a distance d from -Q.The total potential at P due to the charges +q and -Q, using S.I.units is
- (a)
\(\frac { -2Q }{ 9\pi { \epsilon }_{ 0 }{ d }} \)
- (b)
\(\frac { -Q }{ 6\pi { \epsilon }_{ 0 }{ d }} \)
- (c)
\(\frac { +3Q }{ 4\pi { \epsilon }_{ 0 }{ d }} \)
- (d)
\(\frac { +Q }{ 6\pi { \epsilon }_{ 0 }{ d }} \)
A \(3 \mu F\) capacitor is charged by 10 V battery and then discharged through 1M\(\Omega \) resistor.In 3 seconds the potential difference across the capacitor decrease to a vlue in V of about
- (a)
6
- (b)
5
- (c)
8
- (d)
4
The field strength E (x) as a function of x along the axis of a uniformly charged ring is
for a uniformly charged ring, the electric field
\(E(x)=\frac{Qx}{4\pi \epsilon_0(x^{2}+a^{2})^{\frac{3}{2}}}\), along x-axis
- (a)
- (b)
- (c)
- (d)
An electric dipole consists of two equal and opposite charges,+Q and -Q, separated by a fixed distance l.Such a dipole has charge |Q|=\(3 \mu C\)and l=2 cm. The electric field strength at a distance if 1m from the dipole along the dipole axis is \(\frac { 1 }{ 4\pi { \epsilon }_{ 0 } } =9\times { 10 }^{ 9 }N.m.{ C }^{ -2 }\)
- (a)
1080 \({NC} ^ { -1 }\)
- (b)
\(108{NC} ^ { -1 }\)
- (c)
\(540{NC} ^ { -1 }\)
- (d)
\(2160{NC} ^ { -1 }\)
A metal sphere is to be charged to a potential of \({10} ^ {6}\)V.the field strength is not to exceed \(3\times { 10 }^{ 6 }V{ m }^{ -1 }\), the point at which the insulating quality of air breaks down and corona discharge or sparking takes place.The minimum radius of the sphere is
- (a)
37.1 cm
- (b)
33.3 cm
- (c)
50.0 cm
- (d)
None of the above
A metal sphere is to be charged to a potential of \({10} ^ {6}\)V.the field strength is not to exceed \(3\times { 10 }^{ 6 }V{ m }^{ -1 }\)in order to avoid break down of air insulation.The minimum charge on the sphere for such a purpose is [Given \(K=\frac { 1 }{ 4\pi { \epsilon }_{ 0 } } =9\times { 10 }^{ 9 }Nm^{ 2 }.{ C }^{ -2 }\)]
- (a)
\(37.1 \mu C\)
- (b)
\(33.3 \mu C\)
- (c)
\(50.0 \mu C\)
- (d)
None of the above
A parallel plate capacitor can be charged to 3 C before breakdown occurs when air is between the plates.If the space between the plates is filled with glass (dielectric constant=5), then the maximum charge on the plates is
- (a)
135.0 C
- (b)
67.5 C
- (c)
45.0 C
- (d)
15.0 C
Which one of the following graphs shows the variation of electric potential V with distance r from the centre of a hollow charged sphere of radius R?
- (a)
- (b)
- (c)
- (d)
A metal foil of negliable thickness is introduced between two plates of a capacitor at the centre.The capacitance of capacitor will be
- (a)
same
- (b)
double
- (c)
half
- (d)
k times
A capacitor of capacity 2\(\mu F\)is charged to a potential difference of 12 V.it is then connected across an inductance of 0.6mH.the current in amperes across the capacitor is 6V is
- (a)
0.6
- (b)
1.2
- (c)
2.4
- (d)
3.6
Two spheres of radii \({R }_ { 1 }and {R } {2 }\) respectively are charged and joined by a write.The ratio of electric field of spheres is
- (a)
\({ { R }_{ 2 } }^{ 2 }/{ { R }_{ 1 } }^{ 2 }\)
- (b)
\({ { R }_{ 1 } }^{ 2 }/{ { R }_{ 2 } }^{ 2 }\)
- (c)
\( { R }_{ 2 } / { R }_{ 1 } \)
- (d)
\( { R }_{ 1 } / { R }_{ 2 } \)
Two equal point charges are fixed at x=-a and x=+a on the x-axis .Another point charge Q is placed at the orgin.The change in the electrical potential energy of Q,when it is displaced by a small distance x along the x-axis , is approximately proportional to
- (a)
x
- (b)
\({x} ^ { 2} \)
- (c)
\({x}^{3}\)
- (d)
1/x
Two identical conductors of copper and aluminium are placed in an identical electric fields. The magnitude of induced charge in the aluminium will be
- (a)
zero
- (b)
greater than in copper
- (c)
equal to that in copper
- (d)
less that in copper
The electric field at point (30, 30, 0) due to a charge 0.008\(\mu C\) at origin will be (coordinates are in cm)
- (a)
\(8000{ NC }^{ -1 }\)
- (b)
4000 (^ + ^) NC-1
- (c)
200\(\sqrt{2}\)(^ + ^) NC-1
- (d)
400\(\sqrt{2}\)(^ + ^) NC-1
A circular ring carries a uniformly distributed positive charge and lies in XY-plane with the centre at origin of coordinate system. If at a point (0,0,Z) electric field is E, which of the following graphs is correct ?
- (a)
- (b)
- (c)
- (d)
The electrostatic potential inside a charged spherical ball is given by \(\phi =ar^2+b\), where r is the distance from the centre and a, b are constants. Then, the charge density inside the ball is
- (a)
\(-6a\epsilon_0r\)
- (b)
\(-24\pi a\epsilon_0\)
- (c)
\(-6a\epsilon_0\)
- (d)
\(-24\pi a\epsilon_0r\)
Match the physical quantities given in Column I with their formula given in Column II and select the correct option from the choices given below :
Column I | Column II |
A. Torque experienced by electric dipole | 1. \(\frac { W }{ Q } \) |
B. Electric flux | 2. P X E or PE sinQ |
C. Electric potential | 3. E. ds |
- (a)
A B C 1 2 3 - (b)
A B C 2 3 1 - (c)
A B C 3 2 1 - (d)
A B C 3 1 2
Let there be a spherically symmetric charge distribution with charge density varying as \(\rho \left( r \right) ={ \rho }_{ 0 }\left( \frac { 5 }{ 4 } -\frac { r }{ R } \right) \) upto r = R and \(\rho \left( r \right) =0\) for r > R, where r is the distance from the origin. The electric field at a distance r(r
- (a)
\(\frac { 4\pi { \rho }_{ 0 }r }{ 3{ \varepsilon }_{ 0 } } \left( \frac { 5 }{ 3 } -\frac { r }{ R } \right) \)
- (b)
\(\frac { { \rho }_{ 0 }r }{ 4{ \varepsilon }_{ 0 } } \left( \frac { 5 }{ 3 } -\frac { r }{ R } \right) \)
- (c)
\(\frac { 4 { \rho }_{ 0 }r }{ 3{ \varepsilon }_{ 0 } } \left( \frac { 5 }{ 4} -\frac { r }{ R } \right) \)
- (d)
\(\frac { { \rho }_{ 0 }r }{ 3{ \varepsilon }_{ 0 } } \left( \frac { 5 }{ 4 } -\frac { r }{ R } \right) \)
Two points P and Q are maintained at the potentials of 10 V and - 4V, respectively. The work done in moving 100 electron from P to Q is
- (a)
- 19 X 10-17 J
- (b)
9.60 X 10-17 J
- (c)
- 2.24 X 10-16 J
- (d)
2.24 X 10-16 J
A thin spherical shell of radius R has charge Q spread uniformly over its surface. Which of the following graphs most closely represents the electric field E(r) produced by the shell in the range \(0\le r
- (a)
- (b)
- (c)
- (d)
Two spherical conductors A and B of radii 1 mm and 2 mm are separated by a distance of 5 cm and are uniformly charged. If the spheres are connected by a connecting wire, then in equilibrium condition, the radio 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