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Moving Charges & Magnetism revision notes

Every idea in the Moving Charges & Magnetism chapter for JEE Main, with the usual mistakes and the fast methods. Topic 1 is open to everyone; sign in free to read all 27 and download the PDF.

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How we count: 7× asked means 7 past JEE Main questions in the PrepWiser bank needed that concept, and "last" is the latest year one appeared. ★ marks ideas asked 8 or more times.

Lorentz force

Lorentz force
18× asked, last 2026
F⃗=q (E⃗+v⃗×B⃗),∣FB∣=qvBsin⁡θ\vec F = q\,(\vec E + \vec v\times\vec B),\qquad |F_B| = qvB\sin\theta
θ\theta between v⃗\vec v and B⃗\vec B. Use q=−eq=-e for an electron. F⃗B\vec F_B is perpendicular to both v⃗\vec v and B⃗\vec B.
v⃗\vec vB⃗\vec BF⃗=qv⃗×B⃗\vec F=q\vec v\times\vec Bθ\theta+q+qv⃗\vec v–B⃗\vec B plane
F⃗B\vec F_B is normal to the plane of v⃗\vec v and B⃗\vec B; size qvBsin⁡θqvB\sin\theta
  • The magnetic force is perpendicular to B⃗\vec B, so in a pure magnetic field a⃗⋅B⃗=0\vec a\cdot\vec B=0. Use it to find a missing component of a⃗\vec a or B⃗\vec B.
  • v⃗∥B⃗\vec v\parallel\vec B gives no force: a charge moving along a solenoid's axis keeps its velocity, and one dropped along a vertical solenoid's axis falls with a=ga=g.
  • Not i^×k^=+j^\hat i\times\hat k=+\hat j. It is −j^-\hat j (anticyclic order). Expand v⃗×B⃗\vec v\times\vec B as a determinant, minus sign on the j^\hat j term; subtract qE⃗q\vec E first.
Magnetic force does no work
7× asked, last 2026
P=F⃗B⋅v⃗=0,ΔK=∫qE⃗⋅dl⃗P = \vec F_B\cdot\vec v = 0,\qquad \Delta K = \int q\vec E\cdot d\vec l
True in any B⃗\vec B, uniform or not. Speed and KE stay constant; only E⃗\vec E can change them.
  • Not qvBqvB in the energy equation. In combined fields only E⃗\vec E does work: ΔK=∫qE dx\Delta K=\int qE\,dx. The rate of work by E⃗\vec E is qE⃗⋅v⃗q\vec E\cdot\vec v, zero where v⃗⊥E⃗\vec v\perp\vec E.
Velocity selector (crossed E and B)
5× asked, last 2025
qE=qvB  ⇒  v=EBqE = qvB \;\Rightarrow\; v = \frac{E}{B}
E⃗⊥B⃗\vec E\perp\vec B, both perpendicular to v⃗\vec v. Passes undeflected for any qq and mm; only the speed is selected.
++−-v<E/Bv<E/Bv=E/Bv=E/Bv>E/Bv>E/B+q+qE⃗\vec E down, B⃗\vec B into the page
Traced from q(E⃗+v⃗×B⃗)q(\vec E+\vec v\times\vec B): only v=E/Bv=E/B passes straight; slower bends with qE⃗q\vec E, faster with qv⃗×B⃗q\vec v\times\vec B
  • Not a reversed B⃗\vec B for an electron. Flipping qq reverses both qE⃗q\vec E and qv⃗×B⃗q\vec v\times\vec B, so the same fields pass any charge at that velocity. Get v=2K/mv=\sqrt{2K/m} from the KE, then E=vBE=vB.

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Practise Moving Charges & Magnetism

24 more concepts in 6 topics

Charge in a uniform magnetic field; Biot–Savart law; Ampère's law, solenoid and toroid; Force on current-carrying conductors; Current loop as a magnetic dipole; and Moving coil galvanometer and meters. Read the first part free. Sign in free with Google to read the rest and download the PDF.

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Charge in a uniform magnetic field

  • Radius of the circular path18×
  • Period and frequency11×
  • Helical path5×
  • Crossing a field region of width d4×

Biot–Savart law

  • Biot–Savart law4×
  • Finite straight wire11×
  • Infinite and semi-infinite wire16×
  • Regular polygon at its centre8×
  • Arc at its centre13×
  • Circular loop: centre and axis22×

Ampère's law, solenoid and toroid

  • Ampère's circuital law4×
  • Long solid wire9×
  • Hollow cylinder and coaxial cable3×
  • Long solenoid10×

Force on current-carrying conductors

  • Force on a wire12×
  • Force between parallel wires6×
  • Also remember1

Current loop as a magnetic dipole

  • Magnetic moment of a loop8×
  • Torque and energy in a uniform field7×
  • Orbiting or spinning charge3×

Moving coil galvanometer and meters

  • Moving coil galvanometer5×
  • Current and voltage sensitivity7×
  • Figure of merit and half deflection3×
  • Ammeter: galvanometer with a shunt16×
  • Voltmeter: galvanometer with series R8×

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Practise Moving Charges & Magnetism

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