A doubly ionized helium nucleus (charge $= 3.2 \times 10 ^{-19}C$) enters a region of uniform magnetic field with a velocity $(10 ^3 \,m/s).$ $\hat {i}$ The magnetic induction in the region is 20 mT directed towards the positive x-axis. The force on the ion is

$(6.4 \times 10^{-18} N) \ \hat j$

$(6.4 \times 10^{-18} N) \ \hat k$

In a cyclotron, charged particles are accelerated by

the p.d. across the gap between the dees.

the electrostatic deflector plate

the p.d. across the gap between the dees.

$tan^{-1} \ \frac{1}{2\pi} \left(\frac{qB}{m}\right)^2$

$tan^{-1} \ 2\pi \left(\frac{qB}{m}\right)^2$

$(6.4 \times 10^{-18} N) \ \hat j$

the p.d. across the gap between the dees.

Answer these simple questions correctly and earn coins

Difficulty Level :

10 Questions

A doubly ionized helium nucleus (charge $= 3.2 \times 10 ^{-19}C$ ) enters a region of uniform magnetic field with a velocity $(10 ^3 \,m/s).$ $\hat {i}$ The magnetic induction in the region is 20 mT directed towards the positive x-axis. The force on the ion is

If R is the radius of the dees and B the magnitude of the magnetic field induction in which positive charges (q) of mass m escape from the cyclotron, then their maximum speed $v_{max}$ is

A charged particle moving with a velocity $\overrightarrow v$ enters a region of uniform magnetic field $\overrightarrow B$ such that the pitch of the resulting helical motion is equal to the radius of the helix. The angle between $\overrightarrow v$ and $\overrightarrow B$ is

A charged particle enters a uniform magnetic field initially travelling perpendicular to the field lines and is bent in a circular arc of radius R. If the particle had the same charge but double the mass and were travelling twice as fast, the radius of its circular arc would be

A straight wire along the y-axis carries a current of 4 A. The wire is placed in a uniform magnetic field (0.02 T) . If the current in the wire is directed towards the negative y-axis, the force per unit length on the wire is

A 30-turn coil of diameter 2 cm carries a current of 10 mA. When it is placed in a uniform magnetic field of 0.05 T, the magnitude of the maximum torque that could be exerted on the coil by the magnetic field is

A circular loop of area $1 c m^{2}$ and carrying a current of 10 $μ \mu$ A is placed in a magnetic field with its plane parallel to (B = 15 mT). When the loop has rotated through an angle of 45°, the magnitude of the torque exerted on this loop is

A charged particle moving with a velocity $\overrightarrow v$ enters a region of uniform magnetic field $\overrightarrow B$ . If the velocity has a component parallel to $\overrightarrow B$ , which of the following quantities is independent of | $\overrightarrow v$ |?