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Three charges are placed at the vertices of an equilateral triangle of side 'a' as shown in the following figure. The force experienced by the charge placed at the vertex A in a direction normal to BC is
                             
1.  $\frac{{\mathrm{Q}}^2}{\left(4{\mathrm{\pi \epsilon }}_0{\mathrm{a}}^2\right)}$
2.  $\frac{-{\mathrm{Q}}^2}{\left(4{\mathrm{\pi \epsilon }}_0{\mathrm{a}}^2\right)}$
3.  Zero
4.  $\frac{{\mathrm{Q}}^2}{\left(2{\mathrm{\pi \epsilon }}_0{\mathrm{a}}^2\right)}$

The spatial distribution of the electric field due to charges (A, B) is shown in figure. Which one of the following statement is correct?
                       
1.  A is -ve and B +ve; |A|=|B|
2.  Both are +ve but A>B
3.  Both are -ve but A>B
4.  A is +ve and B -ve and |A|>|B|

Three point charges +q, -2q and +q are placed at points (x=0, y=a, z=0), (x=0, y=0, z=0) and (x=a, y=0, z=0), respectively. The magnitude and direction of the electric dipole moment vector of this charge assembly are
1.  $\sqrt{2}\mathrm{qa}$ along +y direction
2.  qa along the line joining points (x=0, y=0, z=0) and (x=a, y=a, z=0)
3.  $\sqrt{2}\mathrm{qa}$ along the line joining points (x=0, y=0, z=0) and (x=a, y=a, z=0)
4.  $\sqrt{2}\mathrm{qa}$ along +x direction

Two point charges +8q and -2q are located at x=0 and x=L respectively. The location of a point on the x-axis at which the net electric field due to these two point charges is zero is
1.  8L
2.  4L
3.  2L
4.  L/4

Three charges $-{\mathrm{q}}_1, +{\mathrm{q}}_2 \mathrm{and} -{\mathrm{q}}_3$ are placed as shown in the figure. The x-component of the force on $-{\mathrm{q}}_1$ is proportional to
                                         
1.  $\frac{{\mathrm{q}}_2}{{\mathrm{b}}^2}-\frac{{\mathrm{q}}_3}{{\mathrm{a}}^2} \mathrm{sin\theta }$
2.  $\frac{{\mathrm{q}}_2}{{\mathrm{b}}^2}-\frac{{\mathrm{q}}_3}{{\mathrm{a}}^2} \mathrm{cos\theta }$
3.  $\frac{{\mathrm{q}}_2}{{\mathrm{b}}^2}+\frac{{\mathrm{q}}_3}{{\mathrm{a}}^2} \mathrm{sin\theta }$
4.  $\frac{{\mathrm{q}}_2}{{\mathrm{b}}^2}+\frac{{\mathrm{q}}_3}{{\mathrm{a}}^2} \mathrm{cos\theta }$

+2C and +6C two charges are repelling each other with a force of 12 N. If each charges is given -2C of charge, then the value of the force will be
1.  4N (Attractive)
2.  4N (Repulsive)
3.  8N (Repulsive)
4.  Zero

Two equal charges are separated by a distance d. A third charge placed on a perpendicular bisector at x distance will experience maximum coulomb force when
1.  $\mathrm{x}=\frac{\mathrm{d}}{\sqrt{2}}$
2.  $\mathrm{x}=\frac{\mathrm{d}}{2}$
3.  $\mathrm{x}=\frac{\mathrm{d}}{2\sqrt{2}}$
4.  $\mathrm{x}=\frac{\mathrm{d}}{2\sqrt{3}}$

Three positive charges of equal value q are placed at the vertices of an equilateral triangle. The resulting lines of force should be sketched as in
1.
2.
3.
4.

There are three concentric thin spheres of radius a, b, c (a>b>c). The total surface charge densities on their surfaces are $\mathrm{\sigma }, -\mathrm{\sigma }, \mathrm{\sigma }$ respectively. The magnitude of electric field at r (distance from centre) such that a>r>b is:
1.  $0$
2.  $\frac{\mathrm{\sigma }}{{\in }_0 {\mathrm{r}}^2} \left({\mathrm{b}}^2-{\mathrm{c}}^2\right)$
3.  $\frac{\mathrm{\sigma }}{{\in }_0 {\mathrm{r}}^2} \left({\mathrm{a}}^2+{\mathrm{b}}^2\right)$
4.  none of these

A ring of radius R, has charge -Q distributed uniformly over it. A charge q is placed at the centre of the ring such that the electric field becomes zero at a point on the axis of the ring distant 'R' from the centre of the ring. The value of charge q is
1.  $\frac{\mathrm{Q}}{2}\sqrt{3}$
2.  $\frac{\mathrm{Q}}{4}\sqrt{2}$
3.  $\frac{\mathrm{Q}}{3}\sqrt{2}$
4.  $\frac{\mathrm{Q}}{4}\sqrt{3}$

The electric field in a certain region is acting radially outward and is given by E=Ar. A charge contained in a sphere of radius 'a' centred at the origin of the field will be given by
1.  $4{\mathrm{\pi \epsilon }}_0{\mathrm{Aa}}^2$
2.  $4{\mathrm{\epsilon }}_0{\mathrm{a}}^2$
3.  $4{\mathrm{\pi \epsilon }}_0{\mathrm{Aa}}^3$
4.  ${\mathrm{\epsilon }}_0{\mathrm{Aa}}^2$

Two pith balls carrying equal charges are suspended from a  common point by strings of equal length, the equilibrium separation between them is r. Now the strings are rigidly clamped at half the height. The equilibrium separation between the balls now become
                   
1.  ${\left(\frac{1}{\sqrt{2}}\right)}^2$
2.  $\left(\frac{\mathrm{r}}{\sqrt[3]{2}}\right)$
3.  $\left(\frac{2\mathrm{r}}{\sqrt{3}}\right)$
4.  $\left(\frac{2\mathrm{r}}{3}\right)$

A charge Q is enclosed by a Gaussian spherical surface of radius R. If the radius is doubled, then the outward electric flux will
1.  be reduced to half
2.  remain the same
3.  be doubled
4.  increase four times

The electric field at a distance 3R/2 from the center of a charged conducting spherical shell of radius R is E. The electric field at a distance R/2 from the center of the sphere is
1.  $\frac{\mathrm{E}}{2}$
2.  zero
3.  $\mathrm{E}$
4.  $\frac{\mathrm{E}}{4}$

A thin conducting ring of radius R is given a charge +Q. The electric field at the centre O of the ring due to the charge on the part AKB of the ring is E. The electric field at the centre due to the charge on the part ACDB of the ring is
                                   
1.  E along KO
2.  E along OK
3.  E along KO
4.  3E along OK

A uniformly charged and infinitely long line having a liner charge density '$\mathrm{\lambda }$' is placed at a normal distance y from a point O. Consider a sphere of radius R with O as centre and R>y. Electric flux through the surface of the sphere is:
                                   
1.  zero
2.  $\frac{2\mathrm{\lambda R}}{{\mathrm{\epsilon }}_0}$
3.  $\frac{2\mathrm{\lambda }\sqrt{{\mathrm{R}}^2-{\mathrm{y}}^2}}{{\mathrm{\epsilon }}_0}$
4.  $\frac{\mathrm{\lambda }\sqrt{{\mathrm{R}}^2+{\mathrm{y}}^2}}{{\mathrm{\epsilon }}_0}$

A point charge +Q is positioned at the centre of the base of a square pyramid as shown. The flux through one of the four identical upper faces of the pyramid is
                                   
1.  $\frac{\mathrm{Q}}{16{\mathrm{\epsilon }}_0}$
2.  $\frac{\mathrm{Q}}{4{\mathrm{\epsilon }}_0}$
3.  $\frac{\mathrm{Q}}{8{\mathrm{\epsilon }}_0}$
4.  None of these

Consider the charge configuration and spherical Gaussian surface as shown in the figure. When calculating the flux of the electric field over the spherical surface the electric field will be due to
                                         
1.  ${\mathrm{q}}_2$
2.  Only the positive charges
3.  All the charges
4.  $+{\mathrm{q}}_1 \mathrm{and} -{\mathrm{q}}_1$

In the  given figure two tiny conducting balls of identical mass m and identical charge q hang from non-conducting threads of equal length L. Assuming that $\mathrm{\theta }$ is so small that tan$\mathrm{\theta }$$\approx$sin$\mathrm{\theta }$, then for equilibrium x is equal to
                                   
1.  ${\left(\frac{{\mathrm{q}}^2\mathrm{L}}{2{\mathrm{\pi \epsilon }}_0 \mathrm{mg}}\right)}^{\frac{1}{3}}$
2.  ${\left(\frac{{\mathrm{qL}}^2}{2{\mathrm{\pi \epsilon }}_0 \mathrm{mg}}\right)}^{\frac{1}{3}}$
3.  ${\left(\frac{{\mathrm{q}}^2{\mathrm{L}}^2}{4{\mathrm{\pi \epsilon }}_0 \mathrm{mg}}\right)}^{\frac{1}{3}}$
4.  ${\left(\frac{{\mathrm{q}}^2\mathrm{L}}{4{\mathrm{\pi \epsilon }}_0 \mathrm{mg}}\right)}^{\frac{1}{3}}$

Assertion: The electric field due to a dipole on its axial line at a distance r is E. Then, electric field due
                to the same dipole on the equatorial line and at the same distance will be $\frac{\mathrm{E}}{2}$.
Reason: Electric field due to dipole varies inversely as the square of distance.

Assertion: When a body acquires positive charge, its mass decreases.
Reason: A body acquires positive charge when it loses electrons.

Assertion: Vehicle carrying highly inflammable materials have hanging chains, slightly touching the ground.
Reason: The body of a vehicle gets charged when moving through air at high speed.

Assertion: The tyres of aircraft's are slightly conducting.
Reason: If a conductor is connected to the ground, the extra charge induced on the conductor will flow to the ground.
1.  Both Assertion & Reason are true and the Reason is the correct explanation of the Assertion.
2.  Both Assertion & Reason are true but the Reason is not the correct explanation of the Assertion.
3.  Assertion is a true statement but Reason is false.
4.  Both Assertion and Reason are false statements.

Assertion: A charged conductor may have charged particle inside it.
Reason: There can't exist electric field lines inside the conductor.