A conducting wire carrying current is  arranged as shown in the figure. The magnetic field at O is

• $\frac{{\mathrm{\mu }}_0\mathrm{i}}{12} \left[\frac{1}{{\mathrm{R}}_1} - \frac{1}{{\mathrm{R}}_2}\right]$

• $\frac{{\mathrm{\mu }}_0\mathrm{i}}{12} \left[\frac{1}{{\mathrm{R}}_1} + \frac{1}{{\mathrm{R}}_2}\right]$

• $\frac{{\mathrm{\mu }}_0\mathrm{i}}{6} \left[\frac{1}{{\mathrm{R}}_1} - \frac{1}{{\mathrm{R}}_2}\right]$

• $\frac{{\mathrm{\mu }}_0\mathrm{i}}{6} \left[\frac{1}{{\mathrm{R}}_1} + \frac{1}{{\mathrm{R}}_2}\right]$

The quantity of a charge that will be transferred by a current flow of 20 A over 1 h 30 min period is

• 10.8 × 10³ C

• 10.8 × 10⁴ C

• 5.4 × 10³ C

• 1.8 × 10⁴ C

A galvanometer coil has a resistance of 50 Ω and the meter shows full scale deflection for a current of 5 mA. This galvanometer is converted into voltmeter of range 0-20 V by connecting

• 3950 Ω in series with galvanometer

• 4050 Ω in series with galvanometer

• 3950 Ω in parallel with galvanometer

• 4050 Ω in parallel with galvanometer

${\mathrm{\chi }}_1$ and ${\mathrm{\chi }}_2$ are susceptibility of a paramagnetic material at temperatures T₁ K and T₂ K respectively, then

• ${\mathrm{\chi }}_1 = {\mathrm{\chi }}_2$

• ${\mathrm{\chi }}_1{\mathrm{T}}_1 = {\mathrm{\chi }}_2{\mathrm{T}}_2$

• ${\mathrm{\chi }}_1{\mathrm{T}}_2 = {\mathrm{\chi }}_1{\mathrm{T}}_1$

• ${\mathrm{\chi }}_1 \sqrt{{\mathrm{T}}_1} = {\mathrm{\chi }}_2 \sqrt{{\mathrm{T}}_2}$

At certain place, the horizontal component of Earth's magnetic field is 3.0 G and the angle dip at that place is 30°. The magnetic field of Earth at that location is

• 4.5 G

• 5.1 G

• 3.5 G

• 6.0 G

A long solenoid with 40 turns per cm carries a current of 1 A. The magnetic energy stored per unit volume is

• $3.2 \mathrm{\pi } {\mathrm{Jm}}^{-3}$

• $32 \mathrm{\pi } {\mathrm{Jm}}^{-3}$

• $1.6 \mathrm{\pi } {\mathrm{Jm}}^{-3}$

• $6.4 \mathrm{\pi } {\mathrm{Jm}}^{-3}$

37.

A wheel with 10 spokes each of length L m is rotated with a uniform angular velocity ω in a plane normal to the magnetic field B. The emf induced between the axle and the rim of the wheel is

• $\frac{1}{2} {\mathrm{N\omega BL}}^2$

• $\frac{1}{2} {\mathrm{\omega BL}}^2$

• ${\mathrm{\omega BL}}^2$

• NωBL²

The rms value of current in a 50 Hz AC circuit is 6 A. The average value of AC current over a cycle is

• $6\sqrt{2}$

• $\frac{3}{\mathrm{\pi }/\sqrt{2}}$

• Zero

• $\frac{6}{\mathrm{\pi }\sqrt{2}}$

A capacitor of capacitance 10 µF is connected to an AC ammeter. If the source voltage varies as $\mathrm{V} = 50\sqrt{2} \sin 100 \mathrm{t}$, the reading of the ammeter is

• 50 mA

• 70.7 mA

• 5.0 mA

• 7.07 mA

In a series L-C-R circuit, the potential drop across L, C and R respectively are 40 V, 120 V and 60 V. Then, the source voltage is

• 220 V

• 160 V

• 180 V

• 100 V