Electric field at the centre of a uniformly charged semicircle of radius a is

• $\frac{\mathrm{\lambda }}{2{\mathrm{\pi \epsilon }}_0{\mathrm{a}}^2}$

• $\frac{\mathrm{\lambda }}{4 {\mathrm{\pi }}^2{\mathrm{\epsilon }}_0 {\mathrm{a}}^2}$

• $\frac{{\mathrm{\lambda }}^2}{2{\mathrm{\pi \epsilon }}_0\mathrm{a}}$

• $\frac{\mathrm{\lambda }}{2{\mathrm{\pi \epsilon }}_0\mathrm{a}}$

If frequency of R-L circuit is f then impedance will be

• $\sqrt{{\mathrm{R}}^2 + {\left( 2\mathrm{\pi fL} \right)}^2}$

• R² + ( 2$\mathrm{\pi }$f² )²

• $\sqrt{\left( {\mathrm{R}}^2 + {\mathrm{L\pi f}}^2 \right)}$

• R² + (2$\mathrm{\pi }$f )²

Two  changes  +q  and  -q  are  attached  to  the  two ends of  a  light rod of length L, as shown in figure. The system is given a velocity  ν  perpendicular to magnetic  field  $\overrightarrow{\mathrm{B}}$. The magnetic force on the system of  charges and magnitude of force on one charge by the rod, are respectively

• zero, zero

• zero, qvB

• 2qvB, 0

• 2qvB,  qvB

The intensity of magnetic field due to an isolated pole of strength m_p at a point distant r from it will be

• m_p/r²

• m_p r²

• r²/ m_p

• m_p/r

A bulb  and  a condenser are connected in with an A>C source. On increasibg the frequency will

• increase

• decrease

• sometimes increase and sometimes decrease

• neither increase nor decrease.

The  ratio of magnetic fields on the axis of a circular current carrying coil of radius a to the magnetic field at its centre will be

• $\frac{1}{{\left(1 + {\displaystyle \frac{{\mathrm{x}}^2}{{\mathrm{a}}^2}}\right)}^{{\displaystyle \raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}}$

• $\frac{1}{{\left(1 + {\displaystyle \frac{{\mathrm{a}}^2}{{\mathrm{x}}^2}}\right)}^{{\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}}$

• $\frac{1}{{\left(1 + {\displaystyle \frac{{\mathrm{a}}^2}{{\mathrm{x}}^2}}\right)}^2}$

• $\frac{1}{{\left(1 + {\displaystyle \frac{{\mathrm{a}}^2}{{\mathrm{x}}^2}}\right)}^3}$

Lumen is the unit of

• Luminous flux

• luminosity

• illumination

• quantity of light

A charge q is uniformly distributed on a ring of radius r. A sphere of an equal radius is constructed with its centre lying on the periphery of the ring. The flux of electric field through the surface of the sphere will be

• $\frac{\mathrm{q}}{{\mathrm{\epsilon }}_0}$

• $\frac{\mathrm{q}}{2{\mathrm{\epsilon }}_0}$

• $\frac{\mathrm{q}}{3{\mathrm{\epsilon }}_0}$

• $\frac{\mathrm{q}}{4{\mathrm{\epsilon }}_0}$

29.

When 100 V d.c  is applied across a coil, a current of 1 A nows through it. When  100 V a.c. of 50 Hz is applied to the same coil only 0.5 A flows. The inductance of the coil is

• 0.55 H

• 5.5 H

• 0.55 mH

• 55 mH

A bulb of 25 W. 200 V and another bulb of 100 W, 200 V are connected in series with a supply line of 220 V. Then

• both bulbs will glow with same brightness

• both bulbs will get fused

• 25 W bulb will glow more brightly

• 100 W bulb will glow more brightly