This chapter connects motion of charged particles with magnetic fields and electromagnetic laws (Biot–Savart, Ampère, Lorentz force), forming a backbone for many board-level problems and competitive-exam questions where multi-step reasoning is tested. Mastery helps in solving practical device problems (cyclotron, velocity selectors, Hall effect) and in using vector methods, integrals and conservation principles that frequently appear in JEE/NEET style questions.
Beyond formula memorisation, this topic tests conceptual clarity about when magnetic forces do or do not work, how steady vs time-varying fields differ (displacement current, induced electric fields), and how spatial non-uniformity changes particle motion—skills that improve both problem-solving speed and accuracy in exams.
15
Minutes
10
Questions
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Marking Scheme
Q1. A proton of mass and charge and an alpha particle of mass and charge are accelerated from rest through the same potential difference . Each then enters a uniform magnetic field perpendicular to its velocity and moves in a circular path of radius (proton) and (alpha). The ratio is:
Q2. Magnetic field measurements taken radially outward from the axis of a long cylindrical conductor of radius carrying steady current show for and for . Which statement is best supported by these measurements?
Q3. A metallic slab of thickness carries a current along its length. When a uniform magnetic field (normal to the slab) is applied, a Hall voltage appears across its width. Assuming charge carriers have charge magnitude , the carrier density (in m) is approximately:
Q4. Statement I: A charged particle moving with velocity parallel to the local magnetic field experiences no magnetic force. Statement II: If the magnetic field is non-uniform, a particle moving parallel to the field can experience a magnetic force that changes its speed.
Q5. In a velocity selector an electron remains undeflected when its speed satisfies . If and , the required electron speed is:
Q6. Two very long, parallel straight conductors separated by carry steady currents and in opposite directions. The magnitude of the magnetic force per unit length between them and its sense (attraction/repulsion) is:
Q7. The axial field of a circular loop of radius carrying current is
At what axial distance does drop to half its central value ? (Numerical value of )
Q8. Statement I: Ampère’s circuital law in the form does not give a unique result for a charging capacitor unless modified. Statement II: Maxwell’s addition of the displacement current term to Ampère’s law restores consistency for time-varying fields and preserves charge conservation.
Q9. A proton moves adiabatically along a magnetic field line. At point A the field magnitude is and its velocity makes a pitch angle with the field. It moves toward a region where increases to . Using conservation of the magnetic moment (total speed constant in purely magnetic forces), the minimum initial pitch angle required for the proton to be reflected before reaching is:
Q10. Statement I: A static magnetic field alone can never change the kinetic energy (speed) of a charged particle. Statement II: A time-varying magnetic field produces an induced electric field which can do work on charges and change their kinetic energy.