CBSE Class 12 Physics Magnetic Effects of Electric Current Advanced Problems

CBSE Class 12 Physics Magnetic Effects of Electric Current Advanced Problems. Please refer to the examination notes which you can use for preparing and revising for exams. These notes will help you to revise the concepts quickly and get good marks.

1. An α- particle is describing a circle of radius 0.45 metre in a field of magnetic induction of 1.2 weber / metre². The mass of a-particle is 6.8 × 10^–27 kg and its charge is twice the charge of electron i.e. 3.2 × 10^–19 coulomb.
(a) Find its speed, frequency of rotation and kinetic energy.
(b) What potential difference is required to accelerate the particle to give this much energy to it?

2. A charge of 1 Coulomb is placed at one end of a non-conducting rod of length 0.6 m. The rod is rotated in a vertical plane about a horizontal axis passing through the other end of the rod with angular frequency 104 π radian / sec. Find the magnetic field at a point on the axis of rotation at a distance of 0.8m from
the centre of the path.

3. An α-particle is accelerated by a potential difference of 104 V. Find the change in its direction of motion, if it enter normally in a region of thickness 0.1 m having transverse
magnetic induction of 0.1 Tesla. (mass of α - particle = 6.4 × 10^–27 kg).

4. There is a constant homogeneous electric field of 100 V / m within the region x = 0 and x = 0.167 m pointing along x direction. There is a constant homogeneous magnetic field B within the region x = 1.67 m and x = 0.334 m pointing along the z-direction. A proton at rest at the origin (x = 0, y = 0) is released. Find the minimum strength of the magnetic field B, so that the proton is detected back at x = 0, y = 0.167 m. (mass of the proton = 1.67 × 10^–27 kg)

5. An electron gun G emits electrons of energy 2keV travelling in the positive x-direction. The electrons are required to hit the spot S, where GS = 0.1 m, and the line GS makes an angle of 60º with the x-axis as shown in the figure. A uniform magnetic field B parallel to GS exists in the region outside the electron gun. Find the minimum value of B needed tomake the electron hit S.

6. A particle of mass 1 × 10^–26 kg and charge + 1.6 × 10^–19 C travelling with a velocity 1.28 × 10⁶ m/s in the +x direction enters a region in which a uniform electric field E and a uniform magnetic field B are present such that E_x = E_y = 0, E_z = – 102.4 kV/m and B_x = B_z = 0, B_y = 8 × 10^–2 Wb /m². The particle enters the region at the origin at time t = 0. Determine the location (x, y and z-coordinates) of the particle at t = 5 × 10^–6 s. If the electric field is switched off at this instant (with magnetic field still present), what will be the position of the particle at t = 7.45 × 10^–6 s?

7. Two long straight parallel wires are 2 m apart, perpendicular to the plane of the paper (see figure). The wire A carries a current of 9.6 A, directed into the plane of the paper. The
wire B carries a current such that the magnetic field of induction at the point P, at a distance of 10/11 m from the wire B, is zero. Find :
(a) The magnitude and direction of the current in B.
(b) The magnitude of the magnetic field of induction at the point S. m
(c) The force per unit length on the wire B.

8. Two circular coils each of 100 turns are held such that one lies in the vertical plane and the other in the horizontal plane with their centres coinciding. The radii of the vertical and horizontal coils are respectively 20 cm and 30 cm. If the directions of the currents in them are such that the earth’s magnetic field at the centre of the coils is exactly neutralised, calculate the currents in each coil [H= 27.8 A/m angle of dip = 30º]

9. Two circular rings each of radius a are joined together such that their planes are perpendicular to each other as shown in the figure. The resistance of each half part of the ring is indicated. A very small loop of mass m and radius r carrying a current I₀ is placed in the plane of the papers at the common centre of the rings. The loop can freely rotate about any of its diametric axes If the loop is slightly displaced, find the time period of its oscillations.

10. Consider a nonconducting plate of radius r and mass m which has a charge q distributed uniformly over it. The plate is rotated about its axis with an angular speed ω. Show that the magnetic moment μ and the angular momentum l of the plate are related as μ = .− q/2m l

11. A current i flows in a long straight wire with cross-section having the form of a thin half ring of radius R as shown in figure. Find the induction of magnetic field at the point O.

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