Science (English Medium) Class 12 - CBSE Question Bank Solutions

Doubly-ionised helium ions are projected with a speed of 10 km s⁻¹ in a direction perpendicular to a uniform magnetic field of magnitude 1.0 T. Find (a) the force acting on an ion (b) the radius of the circle in which it circulates and (c) the time taken by an ion to complete the circle.

A proton is projected with a velocity of 3 × 10⁶ m s⁻¹ perpendicular to a uniform magnetic field of 0.6 T. Find the acceleration of the proton.

The figure shows a convex lens of focal length 12 cm lying in a uniform magnetic field Bof magnitude 1.2 T parallel to its principal axis. A particle with charge 2.0 × 10⁻³ C  and mass 2.0 × 10⁻⁵ kg is projected perpendicular to the plane of the diagram with a speed of 4.8 m s⁻¹. The particle moves along a circle with its centre on the principal axis at a distance of 18 cm from the lens. Show that the image of the particle moves along a circle and find the radius of that circle.

Electrons emitted with negligible speed from an electron gun are accelerated through a potential difference V along the x-axis. These electrons emerge from a narrow hole into a uniform magnetic field B directed along this axis. However, some of the electrons emerging from the hole make slightly divergent angles, as shown in the figure. Show that these paraxial electrons are refocussed on the x-axis at a distance `sqrt(8pi^2mV)/(eB^2).`

Two particles, each with mass m are placed at a separation d in a uniform magnetic field B, as shown in the figure. They have opposite charges of equal magnitude q. At time t = 0, the particles are projected towards each other, each with a speed v. Suppose the Coulomb force between the charges is switched off. (a) Find the maximum value v_mof the projection speed, so that the two particles do not collide. (b) What would be the minimum and maximum separation between the particles if v = v_m/2? (c) At what instant will a collision occur between the particles if v = 2v_m? (d) Suppose v = 2v_m and the collision between the particles is completely inelastic. Describe the motion after the collision.

A uniform magnetic field of magnitude 0.20 T exists in space from east to west. With what speed should a particle of mass 0.010 g and with charge 1.0 × 10⁻⁵ C be projected from south to north so that it moves with uniform velocity?

A particle moves in a circle of diameter 1.0 cm under the action of a magnetic field of 0.40 T. An electric field of 200 V m⁻¹ makes the path straight. Find the charge/mass ratio of the particle.

A particle with a charge of 5.0 µC and a mass of 5.0 × 10⁻¹² kg is projected with a speed of 1.0 km s⁻¹ in a magnetic field of magnitude 5.0 mT. The angle between the magnetic field and the velocity is sin⁻¹ (0.90). Show that the path of the particle will be a helix. Find the diameter of the helix and its pitch.

A proton projected in a magnetic field of 0.020 T travels along a helical path of radius 5.0 cm and pitch 20 cm. Find the components of the velocity of the proton along and perpendicular to the magnetic field. Take the mass of the proton = 1.6 × 10⁻²⁷ kg

A particle of mass m and charge q is released from the origin in a region in which the electric field and magnetic field are given by
`vecB = -B_0 vecj and vecE = E_0 vecK `
Find the speed of the particle as a function of its z-coordinate.

An electron is emitted with negligible speed from the negative plate of a parallel-plate capacitor charged to a potential difference V. The separation between the plates is dand a magnetic field B exists in the space, as shown in the figure. Show that the electron will fail to strike the upper plates if `d > ((2m_eV)/(eB_0^2))^(1/2)`

A long, straight wire carrying a current of 30 A is placed in an external, uniform magnetic field of 4.0 × 10⁻⁴ T parallel to the current. Find the magnitude of the resultant magnetic field at a point 2.0 cm away from the wire.

The plate resistance of a triode is 8 kΩ and the transconductance is 2.5 millimho. (a) If the plate voltage is increased by 48 V and the grid voltage is kept constant, what will be the increase in the plate current? (b) With plate voltage kept constant at this increased value, by how much should the grid voltage be decreased in order to bring the plate current back to its initial value?

Explain how a potential barrier is developed in a p-n junction diode.

Draw the circuit arrangement for studying the V-I characteristics of a p-n junction diode in reverse bias. Plot the V-I characteristics in this case.

Write the important considerations which are to be taken into account while fabricating a p-n junction diode to be used as a Light Emitting Diode (LED). What should be the order of band gap of an LED,  if it is required to emit light in the visible range? Draw a circuit diagram and explain its action. 

Draw the V-I characteristics of an LED. State two advantages of LED lamps over convertional  incandescent lamps. 

Define the dielectric constant of a medium. What is its S.I unit?

Write the important considerations which are to be taken into account while fabricating a p-n junction diode to be used as a Light Emitting Diode (LED). What should be the order of the band gap of an LED, if it is required to emit light in the visible range? Draw a circuit diagram and explain its action.