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Electrostatics

159 Questions Start Allen Test
All Exams Allen
Q26 Allen 3. ELECTRIC FIELD INTENSITY MCQ
The electric field in a certain region is given by $\vec{\mathrm{E}} = (\frac{\mathrm{K}}{\mathrm{x}^3})\hat{\mathrm{i}}$ . The dimensions of K are:-
A.
$\mathrm{MLT^{-3}A^{-1}}$
B.
$\mathrm{ML^{-2}T^{-3}A^{-1}}$
C.
$\mathrm{ML^{4}T^{-3}A^{-1}}$
D.
$\mathrm{M^{\circ}L^{\circ}T^{\circ}A^{\circ}}$
Q27 Allen 3. ELECTRIC FIELD INTENSITY MCQ
Figure below shows regular hexagon, with different charges placed at the vertices. In which of the following cases is the electric field at the centre zero? I II III IV
A.
IV
B.
III
C.
I
D.
II
Q28 Allen 3. ELECTRIC FIELD INTENSITY MCQ
Electric field at the centre 'O' of a semicircle of radius 'a' having linear charge density $\lambda$ is given as :-
A.
$\frac{2\lambda}{\in_0a}$
B.
$\frac{\lambda\pi}{\in_0a}$
C.
$\frac{\lambda}{2\pi\in_0a}$
D.
$\frac{\lambda}{\pi\in_0a}$
Q29 Allen 3. ELECTRIC FIELD INTENSITY MCQ
A semicircular ring of radius 0.5 m is uniformly charged with a total charge of $1.4 \times 10^{-9}$ C. The electric field intensity at the centre of this ring is:-
A.
zero
B.
320 V/m.
C.
64 V/m.
D.
32 V/m.
Q30 Allen 3. ELECTRIC FIELD INTENSITY MCQ
For the given figure the direction of electric field at A will be :
A.
towards AL
B.
towards AY
C.
towards AX
D.
towards AZ
Q31 Allen 3. ELECTRIC FIELD INTENSITY MCQ
$-1 \times 10^{-6}$ C charge is on a drop of water having mass $10^{-6}$ kg. What electric field should be applied on the drop so that it is in the balanced condition with its weight?
A.
10 V/m upward
B.
10 V/m downward
C.
0.1 V/m downward
D.
0.1 V/m upward
Q32 Allen 3. ELECTRIC FIELD INTENSITY MCQ
Two small identical spheres, each of mass 1 g and carrying same charge $10^{-9}$ C are suspended by threads of equal lengths. If the distance between the centres of the spheres is 0.3 cm in equilibrium then the inclination of the thread with the vertical will be:
A.
$\tan^{-1}(0.1)$
B.
$\tan^{-1}(2)$
C.
$\tan^{-1}(1.5)$
D.
$\tan^{-1}(0.6)$
Q33 Allen 4. ELECTRIC FIELD LINES, ELECTRIC FLUX & GAUS'S THEOREM MCQ
Two infinitely long parallel wires having linear charge densities $\lambda_{1}$ and $\lambda_{2}$ respectively are placed at a distance R. The force per unit length on either wire will be:-
A.
$\frac{k2\lambda_1\lambda_2}{R^2}$
B.
$\frac{k2\lambda_1\lambda_2}{R}$
C.
$\frac{k\lambda_1\lambda_2}{R^2}$
D.
$\frac{k\lambda_1\lambda_2}{R}$
Q34 Allen 4. ELECTRIC FIELD LINES, ELECTRIC FLUX & GAUS'S THEOREM MCQ
Choose the correct statement regarding electric lines of force :-
A.
They emerge from negative charge and terminate at positive charge
B.
The electric field in that region is weak where the density of electric lines of force are more
C.
They are in radial directions for a point charge
D.
They have a physical existence
Q35 Allen 4. ELECTRIC FIELD LINES, ELECTRIC FLUX & GAUS'S THEOREM MCQ
A solid sphere of radius R, is charged uniformly with a total charge Q. Then the correct expression for electric field is. (r = distance from centre) :-
A.
$\frac{KQr}{R^{3}}$ , where r < R
B.
$\frac{KQ}{r^{2}}$ , where $r \geq R$
C.
it is zero, at all points
D.
1) and 2) both
Q36 Allen 4. ELECTRIC FIELD LINES, ELECTRIC FLUX & GAUS'S THEOREM MCQ
Which one of the following pattern of electrostatic lines of force is not possible?
A.
B.
C.
D.
image.png
Q37 Allen 4. ELECTRIC FIELD LINES, ELECTRIC FLUX & GAUS'S THEOREM MCQ
A sphere of radius R and charge Q is placed inside a concentric imaginary sphere of radius 2R. The flux associated with the imaginary sphere is:-
A.
$\frac{Q}{\in_0}$
B.
$\frac{Q}{2\in_0}$
C.
$\frac{4Q}{\in_0}$
D.
$\frac{2Q}{\in_0}$
Q38 Allen 4. ELECTRIC FIELD LINES, ELECTRIC FLUX & GAUS'S THEOREM MCQ
A nonconducting solid sphere of radius R is charged uniformly. The magnitude of the electric field due to the sphere at a distance r from its centre :-
(a) increases as r increases, for r < R
(b) decreases as r increases, for 0 < r < āˆž
(c) decreases as r increases, for R < r < āˆž
(d) is discontinuous at r = R
A.
a, c
B.
c, d
C.
a, b
D.
b, d
Q39 Allen 4. ELECTRIC FIELD LINES, ELECTRIC FLUX & GAUS'S THEOREM MCQ
20 Ī¼C charge is placed inside a closed surface; then flux linked with the surface is Ļ†. If 80 Ī¼C charge is put inside the surface then change in flux is :-
A.
4Ļ†
B.
5Ļ†
C.
Ļ†
D.
8Ļ†
Q40 Allen 4. ELECTRIC FIELD LINES, ELECTRIC FLUX & GAUS'S THEOREM MCQ
In a region of space the electric field is given by $\vec{E} = 8\hat{i} +4\hat{j} +3\hat{k}$ . The electric flux through a surface of area of 100 units in the x-y plane is:-
A.
800 units
B.
300 units
C.
400 units
D.
1500 units
Q41 Allen 4. ELECTRIC FIELD LINES, ELECTRIC FLUX & GAUS'S THEOREM MCQ
Electric charge is uniformly distributed over a long straight wire of radius 1 mm. The charge per cm length of the wire is Q coulombs. A cylindrical surface of radius 50 cm and length 1m encloses the wire symmetrically as shown in fig. The total flux passing through the cylindrical surface is:-
A.
$\frac{Q}{\epsilon_0}$
B.
$\frac{100Q}{\epsilon_0}$
C.
$\frac{10Q}{\pi \epsilon_0}$
D.
$\frac{100Q}{\pi \epsilon_0}$
Q42 Allen 4. ELECTRIC FIELD LINES, ELECTRIC FLUX & GAUS'S THEOREM MCQ
Gaus's law is given by $\in_0\oint_{s}\vec{E}.d\vec{s} = q$ , if net charge enclosed by a Gaussian surface is zero then :-
A.
E must be zero on the surface
B.
Number of incoming and outgoing electric lines are equal
C.
there is a net incoming of electric lines
D.
none
Q43 Allen 4. ELECTRIC FIELD LINES, ELECTRIC FLUX & GAUS'S THEOREM MCQ
The electric field is 100 V/m, at a distance of 20 cm from the centre of a dielectric sphere of radius 10 cm. Then E at 3 cm distance from the centre of sphere is :-
A.
100 V/m
B.
125 V/m
C.
120 V/m
D.
zero
Q44 Allen 4. ELECTRIC FIELD LINES, ELECTRIC FLUX & GAUS'S THEOREM MCQ
If the electric flux entering and leaving a closed surface is $\phi_{1}$ and $\phi_{2}$ respectively then electric charge inside the surface will be:
A.
$(\phi_{1} + \phi_{2})\varepsilon_{0}$
B.
$(\phi_{2} - \phi_{1})\varepsilon_{0}$
C.
$\frac{\phi_1 + \phi_2}{\varepsilon_0}$
D.
$\frac{\phi_2 - \phi_1}{\varepsilon_0}$
Q45 Allen 4. ELECTRIC FIELD LINES, ELECTRIC FLUX & GAUS'S THEOREM MCQ
The electric field in a region of space is given by $E = (5\hat{i} + 2\hat{j})$ N/C. The electric flux through an area of $2 \, m^{2}$ lying in the YZ plane, in S.I. units is:-
A.
10
B.
20
C.
$10\sqrt{2}$
D.
$2\sqrt{29}$
Q46 Allen 4. ELECTRIC FIELD LINES, ELECTRIC FLUX & GAUS'S THEOREM MCQ
The total flux associated with the given cube will be- where 'a' is side of the cube:-( $\frac{1}{\epsilon_{0}}=4\pi\times9\times10^{9}$ SI units)
A.
$162\pi \times 10^{-3}\mathrm{Nm}^2 /\mathrm{C}$
B.
$162\pi \times 10^{3}\mathrm{Nm}^{2} / \mathrm{C}$
C.
$162\pi \times 10^{-6}\mathrm{Nm}^2 /\mathrm{C}$
D.
$162\pi \times 10^{6}\mathrm{Nm}^{2} / \mathrm{C}$
Q47 Allen 4. ELECTRIC FIELD LINES, ELECTRIC FLUX & GAUS'S THEOREM MCQ
A point charge is placed at a distance $\frac{a}{2}$ perpendicular to the plane and above the centre of a square of side a. The electric flux through the square is:-
A.
$\frac{q}{\epsilon_{0}}$
B.
$\frac{q}{\pi\epsilon_{0}}$
C.
$\frac{q}{4\epsilon_{0}}$
D.
$\frac{q}{6\epsilon_{0}}$
Q48 Allen 5. ELECTRIC POTENTIAL, EQUIPOTENTIAL SURFACE & RELATION BETWEEN FIELD & POTENTIAL MCQ
As shown in the fig. charges + q and - q are placed at the vertices B and C of an isosceles triangle. The potential at the vertex A is :-
A.
$\frac{1}{4\pi \in_0}\cdot \frac{2q}{\sqrt{a^2 + b^2}}$
B.
zero
C.
$\frac{1}{4\pi \in_0}\cdot \frac{q}{\sqrt{a^2 + b^2}}$
D.
$\frac{1}{4\pi \in_0}\cdot \frac{-q}{\sqrt{a^2 + b^2}}$
Q49 Allen 5. ELECTRIC POTENTIAL, EQUIPOTENTIAL SURFACE & RELATION BETWEEN FIELD & POTENTIAL MCQ
At any point on the perpendicular bisector of the line joining two equal and opposite charges :-
A.
the electric field is zero
B.
the electric potential is zero
C.
the electric potential decreases with increasing distance from their mid point
Q50 Allen 5. ELECTRIC POTENTIAL, EQUIPOTENTIAL SURFACE & RELATION BETWEEN FIELD & POTENTIAL MCQ
What is the electric potential at a distance 'x' from the centre, inside a conducting sphere having a charge Q and radius R?
A.
$\frac{1}{4\pi\in_{0}}\frac{Q}{R}$
B.
$\frac{1}{4\pi\in_{0}}\frac{Q}{x}$
C.
$\frac{1}{4\pi\in_{0}}\cdot\frac{QX}{R^{2}}$
D.
zero