Electric Charges and Fields

The charges on two spheres are + 7 µC and -5C respectively. They experience a force F. If each of them is given an additional charge of -2 µC, then the new force of attraction will

• F

• $\frac{\mathrm{F}}{2}$

• $\frac{\mathrm{F}}{\sqrt{3}}$

• 2F

A square loop ABCD, carrying a current I₂, is placed near and coplanar with a long straight conductor XY carrying a current I₁, as shown in figure. The net force on the loop will be

• $\frac{{\mathrm{\mu }}_0 {\mathrm{I}}_1 {\mathrm{I}}_2}{2 \mathrm{\pi }}$

• $\frac{{\mathrm{\mu }}_0 {\mathrm{I}}_1{\mathrm{I}}_2 \mathrm{L}}{2 \mathrm{\pi }}$

• $\frac{2 {\mathrm{\mu }}_0 {\mathrm{I}}_1{\mathrm{I}}_2 \mathrm{L}}{3 \mathrm{\pi }}$

• $\frac{2{\mathrm{\mu }}_0 {\mathrm{I}}_1 {\mathrm{I}}_2}{3 \mathrm{\pi }}$

Three identical charges are placed at the vertices of an equilateral triangle. The force experienced by each charge, ( if k = 1/4$\mathrm{\pi } {\mathrm{\epsilon }}_0$ ) is

• $2\mathrm{k} \frac{{\mathrm{q}}^2}{{\mathrm{r}}^2}$

• $\frac{\mathrm{k} {\mathrm{q}}^2}{2 {\mathrm{r}}^2}$

• $\sqrt{3} \mathrm{k} \frac{{\mathrm{q}}^2}{{\mathrm{r}}^2}$

• $\frac{\mathrm{k} {\mathrm{q}}^2}{\sqrt{2} {\mathrm{r}}^2}$

The angle of dip at a certain place where the horizontal and vertical components of the earth's magnetic field are equal is

• 30^o

• 75^o

• 60^o

• 45^o

Assertion:  Lines of force are perpendicular to conductor surface.

Reason:  Generally electric field is perpendicular to equipotential surface.

• If both assertion and reason are true and reason is the correct explanation of assertion.

• If both assertion and reason are true but reason is not the correct explanation of assertion.

• If assertion is true but reason is false.

• If both assertion and reason are false.

The force per unit length between two straight conductors separated by a distance of 0.02 m is 2 x 10^-3 N m^-1. The current in one conductor is 10 A and that in the other conductor is

• 20 A

• 5 A

• 2 A

• 10 A

The angle of dip at the poles and the equator respectively are

• 30^o, 60^o

• 0^o, 90^o

• 45^o, 90^o

• 90^o, 0^o

Assertion:  The conductivity of an electrolyte is very low as compared to a metal at room temperature. 

Reason:  The number density of free ions in electrolyte is much smaller as compared to the number density of free electrons in metals. Further, ions drift much more slowly, being heavier.

• If both assertion and reason are true and reason is the correct explanation of assertion.

• If both assertion and reason are true but reason is not the correct explanation of assertion.

• If assertion is true but reason is false.

• If both assertion and reason are false.

A particle of charge q and mass m starts moving from the origin under the action of an electric field $\overrightarrow{\mathrm{E}}$ = E₀$\hat{\mathrm{i}}$  and $\overrightarrow{\mathrm{B}} = {\mathrm{B}}_0 \hat{\mathrm{i}}$ velocity  $\overrightarrow{\mathrm{v}} = {\mathrm{v}}_0\widehat{ \mathrm{j}}$. The speed of the particle will become $\frac{\sqrt{5}}{2} {\mathrm{\nu }}_0$ after a time

• $\frac{\mathrm{m} {\mathrm{\nu }}_0}{\mathrm{q} {\mathrm{E}}_0}$

• $\frac{\mathrm{m} {\mathrm{\nu }}_0}{2\mathrm{q} {\mathrm{E}}_0}$

• $\frac{\sqrt{3} {\mathrm{m\nu }}_0}{2\mathrm{q} {\mathrm{E}}_0}$

• $\frac{\sqrt{5} {\mathrm{m\nu }}_0}{2\mathrm{q} {\mathrm{E}}_0}$

Assertion:  Magnetic lines forms closed loops in nature. 

Reason: Mono-magnetic pole does not exist in nature.

• If both assertion and reason are true and reason is the correct explanation of assertion.

• If both assertion and reason are true but reason is not the correct explanation of assertion.

• If assertion is true but reason is false.

• If both assertion and reason are false.