331.

A straight conductor of length I carrying a current I, is bent in the form of a semicircle. The magnetic field (in tesla) at the centre of the semicircle is

• $\frac{{\mathrm{\pi }}^2\mathrm{I}}{\mathrm{l}} \times {10}^{-7}$

• $\frac{\mathrm{\pi I}}{\mathrm{l}} \times {10}^{-7}$

• $\frac{\mathrm{\pi I}}{{\mathrm{l}}^2} \times {10}^{-7}$

• $\frac{{\mathrm{\pi I}}^2}{\mathrm{l}} \times {10}^{-7}$

Which of the following relation represents Biot-Savart's law ?

• $\overrightarrow{\mathrm{dB} } = \frac{{\mathrm{\mu }}_0}{4\mathrm{\pi }} \frac{{\displaystyle \overrightarrow{\mathrm{dl}} \times \overrightarrow{\mathrm{r}}}}{\mathrm{r}}$

• $\overrightarrow{\mathrm{dB} } = \frac{{\mathrm{\mu }}_0}{4\mathrm{\pi }} \frac{{\displaystyle \overrightarrow{\mathrm{dl}} \times \stackrel{\wedge }{\mathrm{r}}}}{{\mathrm{r}}^3}$

• $\overrightarrow{\mathrm{dB} } = \frac{{\mathrm{\mu }}_0}{4\mathrm{\pi }} \frac{{\displaystyle \overrightarrow{\mathrm{dl}} \times \overrightarrow{\mathrm{r}}}}{{\mathrm{r}}^3}$

• $\overrightarrow{\mathrm{dB} } = \frac{{\mathrm{\mu }}_0}{4\mathrm{\pi }} \frac{{\displaystyle \overrightarrow{\mathrm{dl}} \times \overrightarrow{\mathrm{r}}}}{{\mathrm{r}}^4}$

A 50 cm long conductor AB moves with a speed 4 m/s in a magnetic field B = 0.01 Wb/m² as shown. Find the emf generated and power delivered if resistance of the circuit is 0.1 Ω.

An electron is moving with velocity $\left(2 \hat{\mathrm{i}} + 2 \hat{\mathrm{j}}\right)$ m/s in an electric field of intensity $\overrightarrow{\mathrm{E}} = \hat{\mathrm{i}} + 2 \hat{\mathrm{j}} - 8 \hat{\mathrm{k}}$ volt/m and a magnetic field of $\overrightarrow{\mathrm{B}} = \left(2 \hat{\mathrm{j}} + 3 \hat{\mathrm{k}}\right)$ tesla. Find the magnitude of force on the electron.

The ratio of magnetic field and magnetic moment at the centre of a current carrying circular loop is x. When both the current and radius is doubled the ratio will be

• x/8

• x/4

• x/2

• 2x

Current through ABC and A' B'C' is I. What is the magnetic field at P ? BP = PB' = r (Here C' B' PBC are collinear)

• $\mathrm{B} = \frac{1}{4\mathrm{\pi }} \frac{2\mathrm{I}}{\mathrm{r}}$

• $\mathrm{B} = \frac{{\mathrm{\mu }}_0}{4\mathrm{\pi }} \left(\frac{2\mathrm{I}}{\mathrm{r}}\right)$

• $\mathrm{B} = \frac{{\mathrm{\mu }}_0}{4\mathrm{\pi }} \left(\frac{\mathrm{I}}{\mathrm{r}}\right)$

• Zero

The magnetic field at the point of intersection of diagonals of a square wire loop of side L carrying a current I is

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

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

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

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

A straight wire of length 2 m carries a current of 10 A. If this wire is placed in a uniform magnetic field of 0.15 T making an angle of 45° with the magnetic field, the applied force on the wire will be

• 1.5 N

• 3 N

• $3\sqrt{2} \mathrm{N}$

• $\frac{3}{\sqrt{2}} \mathrm{N}$

A magnetic needle is placed in a uniform magnetic field and is aligned with the field. The needle is now rotated by an angle of 60° and the work done is W. The torque on the magnetic needle at this position is

• $2\sqrt{3} \mathrm{W}$

• $\sqrt{3} \mathrm{W}$

• $\frac{\sqrt{3}}{2} \mathrm{W}$

• $\frac{\sqrt{3}}{4} \mathrm{W}$

When a proton is released from rest in a room, it starts with an initial acceleration a₀ towards west. When it is projected towards north with a speed v₀ it moves with an initial acceleration 3a₀ towards west. The electric and magnetic fields in the room are

• $\frac{{\mathrm{ma}}_0}{\mathrm{e}} \mathrm{west}, \frac{2{\mathrm{ma}}_0}{{\mathrm{ev}}_0} \mathrm{up}$

• $\frac{{\mathrm{ma}}_0}{\mathrm{e}} \mathrm{west}, \frac{2{\mathrm{ma}}_0}{{\mathrm{ev}}_0} \mathrm{down}$

• $\frac{{\mathrm{ma}}_0}{\mathrm{e}} \mathrm{east}, \frac{3{\mathrm{ma}}_0}{{\mathrm{ev}}_0} \mathrm{up}$

• $\frac{{\mathrm{ma}}_0}{\mathrm{e}} \mathrm{east}, \frac{3{\mathrm{ma}}_0}{{\mathrm{ev}}_0} \mathrm{down}$