A proton, a deuteron and an α-particle having the same kinetic energy are moving in circular trajectories in a constant magnetic field. If r_p, r_d and r_α denote respectively the radii of the trajectories of these particles, then

• r_α = r_d > r_p

• r_α = r_d = r_p

• r_α < r_d < r_p

• r_α = r_p > r_d

A solenoid has core of a material with relative permeability 500 and its windings carry a current of 1 A. The number of turns of the solenoid is 500 m^-1. The magnetization of the material is nearly

• 2.5 × 10³ Am^-1

• 2.5 × 10⁵ Am^-1

• 2.0 × 10³ Am^-1

• 2.0 × 10⁵ Am^-1

A 2 µC charge moving around a circle with a frequency of 6.25 x 10¹² Hz produces a magnetic field 6.28 T at the centre of the circle. The radius of the circle is

• 2.25 m

• 0.25 m

• 13.0 m

• 1.25 m

A galvanometer of resistance 100 Ω is converted to a voltmeter of range 10 V by connecting a resistance of 10 kΩ. The resistance required to convert the same galvanometer to an ammeter of range 1 A is

• 0.4 Ω

• 0.3 Ω

• 0.1 Ω

• 0.2 Ω

Two wires with currents 2 A and 1 A are enclosed in a circular loop. Another wire with current 3 A is situated outside the loop as shown. Then $\oint \overrightarrow{\mathrm{B}} . \overrightarrow{\mathrm{dl}}$ around the loop is

• µ₀

• 3 µ₀

• 6 µ₀

• 2 µ₀

66.

A current I enters a circular coil of radius R, branches into two parts and then recombines as shown in the circuit diagram

               

The resultant magnetic field at the centre of the coil is

• zero

• $\frac{{\mathrm{\mu }}_0\mathrm{I}}{2\mathrm{R}}$

• $\frac{3}{4} \left(\frac{{\mathrm{\mu }}_0\mathrm{I}}{2\mathrm{R}}\right)$

• $\frac{1}{4} \left(\frac{{\mathrm{\mu }}_0\mathrm{I}}{2\mathrm{R}}\right)$

The resistance of a galvanometer is 50 Ω and it shows full scale deflection for a current of 1 mA. To convert it into a voltmeter to measure 1 V and as well as 10 V (Refer circuit diagram) the resistances R₁ and R₂ respectively are

• 950 Ω and 9150 Ω

• 900 Ω and 9950 Ω

• 900 Ω and 9900 Ω

• 950 Ω and 9000 Ω

Two long parallel wires carry currents i₁ and i₂ such that i₁ >i₂. When the currents are in the same direction, the magnetic field at a point midway between the wires is 6 x 10^-6 T. If the direction of i₂ is reversed, the field becomes 3 x 10^-5 T. The ratio $\frac{{\mathrm{i}}_1}{{\mathrm{i}}_2}$ is

• $\frac{1}{2}$

• 2

• $\frac{2}{3}$

• $\frac{3}{2}$

A coil of 100 turns and area 2 x 10^-2 m², pivoted about a vertical diameter in a uniform magnetic field carries a current of 5A. When the coil is held with its plane in North-South direction, it experiences a torque of 0. 3 Nm. When the plane is in East-West direction the torque is 0.4 Nm. The value of magnetic induction is (Neglect earth's magnetic field)

• 0.2 T

• 0.3 T

• 0.05 T

• 0.1 T

Two particles of equal charges after being accelerated through the same potential difference enter a uniform transverse magnetic field and describe circular path of radii R₁ and R₂ respectively. Then the ratio of their masses (M₁/M₂)
(M,/M,) i

• $\frac{{\mathrm{R}}_1}{{\mathrm{R}}_2}$

• ${\left(\frac{{\mathrm{R}}_1}{{\mathrm{R}}_2}\right)}^2$

• $\frac{{\mathrm{R}}_2}{{\mathrm{R}}_1}$

• ${\left(\frac{{\mathrm{R}}_2}{{\mathrm{R}}_1}\right)}^2$