PUC Science 2nd PUC Class 12 - Karnataka Board PUC Question Bank Solutions for Physics

A current i is passed through a silver strip of width d and area of cross-section A. The number of free electrons per unit volume is n. (a) Find the drift velocity v of the electrons. (b) If a magnetic field B exists in the region, as shown in the figure, what is the average magnetic force on the free electrons? (c) Due to the magnetic force, the free electrons get accumulated on one side of the conductor along its length. This produces a transverse electric field in the conductor, which opposes the magnetic force on the electrons. Find the magnitude of the electric field which will stop further accumulation of electrons. (d) What will be the potential difference developed across the width of the conductor due to the electron-accumulation? The appearance of a transverse emf, when a current-carrying wire is placed in a magnetic field, is called Hall effect.

A particle of charge 2.0 × 10⁻⁸ C and mass 2.0 × 10⁻¹⁰ g is projected with a speed of 2.0 × 10³ m s⁻¹ in a region with a uniform magnetic field of 0.10 T. The velocity is perpendicular to the field. Find the radius of the circle formed by the particle and also the time period.

A proton describes a circle of radius 1 cm in a magnetic field of strength 0.10 T. What would be the radius of the circle described by an α-particle moving with the same speed in the same magnetic field?

An electron of kinetic energy 100 eV circulates in a path of radius 10 cm in a magnetic field. Find the magnetic field and the number of revolutions per second made by the electron.

A circular coil of radius 2.0 cm has 500 turns and carries a current of 1.0 A. Its axis makes an angle of 30° with the uniform magnetic field of magnitude 0.40 T that exists in the space. Find the torque acting on the coil.

A square coil of edge l and with n turns carries a current i. It is kept on a smooth horizontal plate. A uniform magnetic field B exists parallel to an edge. The total mass of the coil is M. What should be the minimum value of B for which the coil will start tipping over?

Consider a non-conducting ring of radius r and mass m that has a total charge qdistributed uniformly on it. The ring is rotated about its axis with an angular speed ω. (a) Find the equivalent electric current in the ring. (b) Find the magnetic moment µ of the ring. (c) Show that `pi = (q)/(2m)` l, where l is the angular momentum of the ring about its axis of rotation.

A charged particle is accelerated through a potential difference of 12 kV and acquires a speed of 1.0 × 10⁶ m s⁻¹. It is then injected perpendicularly into a magnetic field of strength 0.2 T. Find the radius of the circle described by it.

A particle of mass m and positive charge q, moving with a uniform velocity v, enters a magnetic field B, as shown in the figure. (a) Find the radius of the circular arc it describes in the magnetic field. (b) Find the angle subtended by the arc at the centre. (c) How long does the particle stay inside the magnetic field? (d) Solve the three parts of the above problem if the charge q on the particle is negative.

A particle of mass m and charge q is projected into a region that has a perpendicular magnetic field B. Find the angle of deviation (figure) of the particle as it comes out of the magnetic field if the width d of the region is very slightly smaller than 

(a) `(mv)/(qB)`  (b)`(mv)/(2qB)` (c)`(2mv)/(qB)`

A narrow beam of singly-charged carbon ions, moving at a constant velocity of 6.0 × 10⁴m s⁻¹, is sent perpendicularly in a rectangular region of uniform magnetic field B = 0.5 T (figure). It is found that two beams emerge from the field in the backward direction, the separations from the incident beam being 3.0 cm and 3.5 cm. Identify the isotopes present in the ion beam. Take the mass of an ion = A(1.6 × 10⁻²⁷) kg, where A is the mass number.

A narrow beam of singly charged potassium ions of kinetic energy 32 keV is injected into a region of width 1.00 cm with a magnetic field of strength 0.500 T, as shown in the figure. The ions are collected at a screen 95.5 cm away from the field region. If the beam contains isotopes of atomic weights 39 and 41, find the separation between the points where these isotopes strike the screen. Take the mass of a potassium ion = A (1.6 × 10⁻²⁷) kg, where A is the mass number.

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.