This chapter is central to Class 12 Physics because it links motion of charges with electric and magnetic effects—leading to core ideas like magnetic force, circular/helical motion, magnetic fields due to currents, and electromagnetic induction–style energy/force balance (e.g., braking). It is heavily asked in board exams and repeatedly tested in competitive exams through numerical problems and conceptual reasoning.
20
Minutes
15
Questions
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Marking
Q1. An electron is accelerated from rest through a potential difference and then enters a region of uniform magnetic field with its velocity perpendicular to . (Take , .) The radius of the circular path is closest to:
Q2. An –particle (mass , charge ) has kinetic energy and enters a uniform magnetic field with its velocity making an angle with the field. Using , calculate the radius of the helical path (due to the perpendicular component) and the pitch (distance advanced along the field in one revolution).
Q3. A long straight wire carries current upward. A rectangular loop of height and width lies in the same plane; its nearest vertical side is at distance from the wire. The loop carries current such that the current in the side nearest the wire also flows upward (i.e. same direction as the wire in that segment). Using for parallel currents, the net magnetic force on the loop is:
toward the wire
away from the wire
toward the wire
toward the wire
Q4. A conducting rod of mass and length slides without friction on parallel rails forming a closed circuit with resistance . A uniform magnetic field is perpendicular to the plane of the rails. A constant horizontal force pulls the rod to the right. Accounting for the motional emf and the magnetic braking force , find (i) the terminal speed and (ii) the time constant for approach to (starting from rest).
Q5. A proton (mass , charge ) and an alpha particle (mass , charge ) are given the same kinetic energy and then enter a uniform magnetic field perpendicular to their velocities. Using and , which statement is correct?
Their radii are equal; the alpha's cyclotron frequency is half that of the proton.
Their radii are equal; the alpha and proton have the same cyclotron frequency.
The alpha's radius is half the proton's; the alpha and proton have the same cyclotron frequency.
The proton's radius is twice the alpha's; the alpha's cyclotron frequency is half that of the proton.
Q6. An electron with speed moves through a uniform magnetic field of magnitude . Its velocity makes an angle of with the field. What is the magnitude of the magnetic force on the electron? (Take .)
Q7. An electron is accelerated from rest through a potential difference and then enters a uniform magnetic field such that the angle between its velocity and the field is . Calculate the radius of the circular component of its helical path (i.e. radius corresponding to the velocity component perpendicular to the field). (Use and .)
Q8. A conducting rod of length slides without friction on two parallel horizontal conducting rails connected by a resistor , forming a closed circuit. A uniform magnetic field is directed into the plane of the rails. A constant horizontal force is applied to the rod; after transients it moves with constant speed . Assuming motional emf and steady current, determine .
Q9. A proton (, ) moves along the -axis with speed and enters a region between and where a uniform magnetic field points in the -direction. If , find the transverse () displacement of the proton when it exits the region at (neglect edge effects).
Q10. A very long straight wire carries a steady current to the right and also has a uniform positive linear charge density . A positive test charge moves parallel to the wire (in the same direction as ) at distance from the wire with speed . For what value of (in terms of ) will the net radial force on the moving charge be zero?
Q11. A proton of mass and charge enters a uniform magnetic field of magnitude with speed at an angle to the field. What is the radius of the circular motion due to the component of velocity perpendicular to the field?
Q12. A long straight wire carries current . A rectangular loop of width (side parallel to the wire) and height lies coaxial and coplanar with the wire so that the side of the loop closest to the wire is at distance from it. The loop carries current with the current in the nearer side flowing in the same direction as in the straight wire. Neglecting forces on the short sides, the net magnetic force on the entire rectangular loop is:
toward the wire
toward the wire
away from the wire
toward the wire
Q13. A proton (, ) moves with velocity along the -axis and enters a region where a uniform magnetic field of magnitude points into the page. The region length is . If the proton's velocity is perpendicular to , the vertical deflection of the proton on emerging from the magnetic region is approximately:
Q14. A long solid cylindrical conductor of radius carries a total current distributed so that the current density varies with radius as for (and for ). Using Ampère's law, the magnetic field at radial distance (inside the conductor) has magnitude and direction:
Q15. An alpha particle (mass , charge ) and a deuteron (mass , charge ) are each accelerated from rest through the same potential difference and then enter a uniform magnetic field perpendicular to their velocities. If and are their radii of curvature in the magnetic field, which statement is correct?