Moving Charges And Magnetism

An electron of mass m and charge q is travelling with a speed v along a circular path of radius r at right angles to a uniform of magnetic field B. If speed of the electron is doubled and the magnetic field is halved, then resulting path would have a radius of

• $\frac{\mathrm{r}}{4}$

• $\frac{\mathrm{r}}{2}$

• 2r

• 4r

A particle of charge -16 x 10^-18 moving with velocity 10 ms^-1 along the x-axis enters a region where a magnetic field of induction B is along the y-axis, and an electric field of magnitude 10⁴ Vm^-1 is along the negative z-axis. If the charged particle continues moving along the x-axis, then magnitude of B is

• 10^-3 Wbm^-2

• 10³ Wbm^-2

• 10⁵ Wbm^-2

• 10¹⁶ Wbm^-2

The ratio of voltage sensitivity (V_S ) and current sensitivity (I_S ) of a moving coil galvanometer is

• $\frac{1}{\mathrm{G}}$

• $\frac{1}{{\mathrm{G}}^2}$

• G

• G²

A galvanometer acting as a voltmeter should have

• low resistance in series with its coil

• low resistance in parallel with its coil

• high resistance in series with its coil

• high resistance in parallel with its coil

In a region, steady and uniform electric and magnetic fields are present. These two fields are parallel to each other. A charged particle is released from rest in this region. The path of the particle will be a

• helix

• straight line

• ellipse

• circle

The coil in a tangent galvanometer is 16 cm in radius. If a current of 20 mA is to produce a deflection of 45°, then the number of turns wound on it, is (Take horizontal component of earth's magnetic field = 0.36 x 10^-4 T  and µ₀ = 4π x 10^-7 WbA^-1 m^-1 )

• 229

• 458

• 689

• 916

An $\mathrm{\alpha }$-particle with a specific charge of 2.5 × 10⁷ C-kg^-1 moves with a speed of 2 × 10⁵ ms^-1 in a perpendicular magnetic field of 0.05 T. Then the radius of the circular path described by it is

• 8 cm

• 4 cm

• 16 cm

• 2 cm

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.