A galvanometer of resistance, G, is shunted by a resistance S ohm. To keep the main current in the circuit unchanged, the resistance to be put in series with the galvanometer is

1. $\frac{G}{(S+G)}$

2. $\frac{{\mathrm{S}}^2}{(S+G)}$

3. $\frac{SG}{(S+G)}$

4. $\frac{G^{\mathit{2}}}{(S+G)}$

When a proton is released from rest in a room, it starts with an initial acceleration ${\mathrm{a}}_0$ towards west. When it is projected towards north with a speed ${\mathrm{v}}_0$ it moves with an initial acceleration $3{\mathrm{a}}_0$ toward west. The electric and magnetic field in the room are

1. $\frac{m{a}_0}{e}west,<mspace\; width="1em"></mspace>\frac{2m{a}_0}{e{v}_0}up$

2. $\frac{m{a}_0}{e}west,<mspace\; width="1em"></mspace>\frac{2m{a}_0}{e{v}_0}down$

3. $\frac{m{a}_0}{e}east,<mspace\; width="1em"></mspace>\frac{3m{a}_0}{e{v}_0}up$

4. $\frac{m{a}_0}{e}east,<mspace\; width="1em"></mspace>\frac{\mathit{3}m{a}_0}{e{v}_0}\mathrm{down}$

In an ammeter 0.2% of main current passes through the galvanometer. IF the resistance of galvanometer is G, the resistance of ammeter will be

1. $\frac{1}{499}G$

2. $\frac{499}{500}G$

3. $\frac{1}{500}G$

4. $\frac{500}{499}G$

An electron moving in a circular orbit of radius r makes n rotations per second. The magnetic field produced at the centre has magnitude

1. zero

2. $\frac{{\mathrm{\mu }}_0{\mathrm{\pi }}^2\mathrm{e}}{\mathrm{r}}$

3. $\frac{{\mathrm{\mu }}_0\mathrm{ne}}{2\mathrm{r}}$

4. $\frac{{\mathrm{\mu }}_0\mathrm{ne}}{2\mathrm{\pi r}}$

A square loop ABCD carrying a current i is placed near  coplanar long straight conductor XY carrying a current I. The net force on the loop will be -

1. $\frac{2{\mu }_{0}Ii}{3\pi }$

2. $\frac{{\mu }_{0}Ii}{\mathit{2}\pi }$

3. $\frac{2{\mu }_{0}Ii}{3\pi L}$

4. $\frac{{\mu }_{0}Ii}{\mathit{2}\pi L}$

Charge q is uniformly spread on a thin ring of radius R. The ring rotates about its axis with a uniform frequency f Hz. The magnitude of magnetic induction of the centre of the ring is

1. $\frac{{\mathrm{\mu }}_0\mathrm{qf}}{2\mathrm{\pi R}}$

2. $\frac{{\mathrm{\mu }}_0\mathrm{qf}}{2R}$

3. $\frac{{\mathrm{\mu }}_0\mathrm{q}}{2\mathrm{fR}}$

4. $\frac{{\mathrm{\mu }}_0\mathrm{q}}{2\mathrm{\pi fR}}$

A current loop consists of two identical semicircular parts each of radius R, one lying in the x-y plane and the other in y-z plane. If the current in the loop is i, then, the resultant magnetic field due to the two semicircular parts at their common center is

1. $\frac{{\mathrm{\mu }}_0\mathrm{i}}{2\mathrm{R}}$

2. $\frac{{\mathrm{\mu }}_0\mathrm{i}}{4\mathrm{R}}$

3. $\frac{{\mathrm{\mu }}_0\mathrm{i}}{\sqrt{2\mathrm{R}}}$

4. $\frac{{\mathrm{\mu }}_0\mathrm{i}}{2\sqrt{2\mathrm{R}}}$

A galvanometer has a coil of resistance 100 ohm and gives a full scale deflection for a 30 mA current. If it is used as a voltmeter of 30 volt range, the resistance required to be added will be

1. $1000\mathrm{\Omega }$

2. $900\mathrm{\Omega }$

3. $1800\mathrm{\Omega }$

4. $500\mathrm{\Omega }$

A galvanometer having a coil resistance of $60\mathrm{\Omega }$ shows full scale deflection when a current of 1.0 A passes through it. It can be converted into an ammeter to read current up to 5.0A by

1. putting in series a resistance of $15\mathrm{\Omega }$.

2. putting in series a resistance of $240\mathrm{\Omega }$.

3. putting in parallel a resistance of $15\mathrm{\Omega }$.

4. putting in parallel a resistance of $240\mathrm{\Omega }$.

When a charged particle moving with velocity $\overrightarrow{\mathrm{v}}$ is subjected to a magnetic field of induction $\overrightarrow{\mathrm{B}}$, the force on it is non-zero. This implies the

1. angle between $\overrightarrow{\mathrm{v}}<mspace\; width="1em"></mspace>and<mspace\; width="1em"></mspace>\overrightarrow{B}$ is necessary $90°$.

2. angle between $\overrightarrow{\mathrm{v}}<mspace\; width="1em"></mspace>and<mspace\; width="1em"></mspace>\overrightarrow{B}$ can have any value other than $90°$.

3. angle between $\overrightarrow{\mathrm{v}}<mspace\; width="1em"></mspace>and<mspace\; width="1em"></mspace>\overrightarrow{B}$ can have any other value than zero and $180°$.

4. angles between $\overrightarrow{\mathrm{v}}<mspace\; width="1em"></mspace>and<mspace\; width="1em"></mspace>\overrightarrow{B}$ is either zero or $180°$.