Two sources of equal emf are connected to an external resistance R. The internal resistances of the two sources are R₁ and R₂ (R₂>R₁). If the potential difference across the source having internal resistance R₂ is zero, then

• 

• R = R₂-R₁

• 
• 

An electron, a proton and an alpha particle having the same kinetic energy are moving in circular orbits of radii r_e, r_p, r_∝ respectively in a uniform magnetic field B. The relation between r_e, r_p, r_∝ is:

• r_e < r_∝ < r_p

• r_e > r_p =  r_∝

• r_e < r_p =  r_∝

• r_e < r_p <  r_∝

A proton moves with a speed of 5.0 x 10⁶ m/s along the x-axis. It enters a region where there is a magnetic field of magnitude 2.0 Tesla directed at an angle of 30° to the
x-axis and lying in the xy-plane. The magnitude of the magnetic force on the proton is

• 0.8 × 10^-13 N

• 1.6 × 10^-13 N

• 8.0 × 10^-13 N

• 8.01 × 10^-13 N

A long straight wire of radius R carries a steady current I₀, uniformly distributed throughout the cross-section of the wire. The magnetic field at a radial distance r from the centre of the wire, in the region r > R, is

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

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

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

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

If the cyclotron oscillator frequency is 16 MHz, then what should be the operating magnetic field for accelerating the proton of mass 1.67 x 10^-27 kg ?

• 0.334 πT

• 3.34 πT

• 33.4 πT

• 334 πT

If a magnet is dropped through a vertical hollow copper tube, then

• the time taken to reach the ground is longer than the time taken, if the tube was made out of plastic

• the magnet will get attracted and stick to the copper tube

• the time taken to reach the ground is longer than the time taken, if the tube was made out of stainless steel

• the time taken to reach the ground does not depend on the radius of the copper tube

Consider a circular wire loop of radius R spinning about a diametrical chord which is perpendicular to uniform magnetic field $\left({\mathrm{B}}_0\hat{\mathrm{k}}\right)$

• The magnitude of the induced EMF in the loop is maximum when the plane of the loop is perpendicular to B

• Flux through the loop is maximum when the plane of the loop is perpendicular to B

• The direction of induced current remains same during the spinning motion of the loop

• EMF induced will be the same for a larger radius of the loop in the same field

A galvanometer of resistance G is converted into an ammeter using a shunt of resistance R. If the ratio of the heat dissipated through the galvanometer and shunt is 3 : 4, then R equals

• $\frac{4}{3} \mathrm{G}$

• $\frac{3}{4} \mathrm{G}$

• $\frac{16}{9} \mathrm{G}$

• $\frac{9}{16} \mathrm{G}$

The wire of length l is bent into a circular loop of a single turn and is suspended in a magnetic field of induction B. When a current I is passed. through the loop, the maximum torque experienced by it is

• $\left(\frac{1}{4\mathrm{\pi }}\right)$ BIl²

• $\frac{1}{4\mathrm{\pi }}$ BI²l

• $\left(\frac{1}{4\mathrm{\pi }}\right)$ BIl

• $\left(\frac{1}{4\mathrm{\pi }}\right)$ B²Il

40.

A particle having charge 10 times that of the electron revolves in a circular path of radius 0.4 m with an angular speed of one rotation per second. The magnetic induction produced at the centre of the circular path is

• $4\mathrm{\pi } \times {10}^{-26} \mathrm{T}$

• $2\mathrm{\pi } \times {10}^{-26} \mathrm{T}$

• $16\mathrm{\pi } \times {10}^{-26} \mathrm{T}$

• $8\mathrm{\pi } \times {10}^{-25} \mathrm{T}$