This chapter is crucial because it links core ideas of magnetic force with high-value problems on circular/helical motion, Hall effect, and magnetic fields from conductors. These concepts repeatedly appear in CBSE board exams (for conceptual reasoning and numerical derivations) and in competitive exams (for identifying the correct force/field relations and applying them in multi-step situations like magnetic mirrors and mixed field regions).
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15
Questions
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Marking
Q1. A proton and an alpha particle, each having the same kinetic energy , enter a region of uniform magnetic field with their velocities perpendicular to . If and are the radii of their circular trajectories, the ratio is
Q2. A charged particle moves in a uniform magnetic field and its trajectory is a helix. If the pitch (distance moved along in one revolution) equals the circumference of the circular projection, the angle between its velocity and the field is
Q3. A conducting rod of length and mass slides without friction on conducting rails that make an angle with the horizontal. The rod and rails form a closed circuit of resistance . A uniform magnetic field is directed into the plane of the rails. After transients the rod attains a steady terminal speed down the incline when magnetic damping balances the component of gravity. The terminal speed (approximately) is
Q4. A rectangular metallic slab of thickness carries a current along its length. A uniform magnetic field is applied perpendicular to the slab, producing a Hall voltage across the thickness. If the charge carrier density is and the electronic charge is , the magnitude of the Hall voltage across the slab is closest to
Q5. A thin wire consists of a semicircular arc of radius joined smoothly to a very long straight segment which is tangent to the arc at one end. A steady current flows through the wire. The magnitude of the magnetic field at the centre of the semicircular arc is
Q6. An electron () moves with speed in a uniform magnetic field . Its velocity makes an angle with . The magnitude of the magnetic force on the electron is:
Q7. A rectangular metallic slab carries a current along its length. The distance between the faces where Hall voltage is measured is and the slab thickness is . A perpendicular magnetic field produces a measured Hall voltage . Assuming charge carriers are electrons of charge magnitude , the carrier density is closest to:
Q8. Two identical point charges each of charge move in vacuum along two parallel straight lines separated by a distance , both moving in the same direction with speed . Find the speed (use ) for which the magnetic attraction between them has magnitude equal to half the electrostatic repulsion.
Q9. A rectangular loop ABCD of width and height lies in the plane of the paper with its centre at the origin; its vertical sides are at and horizontal sides at . A uniform magnetic field exists only in the region and is zero for . A current flows anticlockwise around the loop (from A at to B at , etc.). If , , and , the net magnetic force on the loop is:
to the right
to the left
to the right
Q10. A proton (, ) has speed and enters a uniform magnetic field with its velocity making an angle with . After the proton completes full revolutions about the field lines, the distance it has moved parallel to is closest to:
Q11. A proton (mass , charge ) has kinetic energy and enters a uniform magnetic field with its velocity perpendicular to . Using the relation , the radius of its circular path is closest to
Q12. A proton with speed enters a region of uniform magnetic field at an angle to the field direction. The pitch (distance advanced along the field in one full revolution) is with . The numerical value of the pitch is about
Q13. A long straight cylindrical conductor of radius carries total current with a radially varying current density for . Using Ampère's law and the relation between and , the magnetic field magnitude at a distance from the axis is
Q14. Consider the two statements:
Statement A: "For a charged particle moving in a static magnetic field the Lorentz force does no work, so the particle's kinetic energy (and speed) cannot change."
Statement B: "If the magnetic field varies with time, Faraday induction produces an electric field which can do work on the charge and change its kinetic energy." Which of the following is correct?
Both statements A and B are true and B correctly explains A.
Both statements A and B are true but B does not correctly explain A.
Statement A is true and B is false.
Statement A is false and B is true.
Q15. A singly charged ion moves into a region where the magnetic field magnitude slowly increases from to along the field direction. The ion's initial velocity makes an angle with the initial field. Will the ion be reflected (magnetic mirror) by the increasing field?
No; the mirror condition is , so is insufficient.
Yes; as increases the perpendicular speed grows and reflection occurs once .
Yes; the changing induces an electric field that reverses the parallel velocity, producing reflection.
No; magnetic forces cannot change the component of velocity parallel to the magnetic field, so reflection is impossible.