Class 12 Physics · NCERT notes for NEET

Moving Charges and Magnetism: NCERT Notes, Formulas and Tricks for NEET

How currents make magnetic fields and how those fields push on moving charges, wires and coils, ending with the moving coil galvanometer. NEET regularly asks from it: radius and period of circular motion, fields of wires, loops and solenoids, force between wires and meter conversion.

1. Magnetic force on moving charges
2. Biot-Savart law 🔒
3. Ampere's circuital law and solenoids 🔒
4. Force and torque on current carrying conductors 🔒
5. Moving coil galvanometer 🔒

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Topic 1

Magnetic force on moving charges

The aurora is charged particles from the Sun spiralling along Earth's field lines into the polar sky. A magnetic field can steer a charge, but it can never speed it up.

Oersted (1820) saw a compass needle deflect near a current-carrying wire: moving charges produce a magnetic field.
Force on a charge $q$ moving with $v$ in field $B$ : $F = q (v \times B)$ , size $q v B sin θ$ . With an electric field too, the Lorentz force is $F = q (E + v \times B)$ .
The magnetic force is zero if the charge is at rest or moves along $B$ ( $θ = 0$ or $18 0^{\circ}$ ). It is largest, $q v B$ , when $v ⊥ B$ .
$F ⊥ v$ always, so the magnetic force does no work: speed and kinetic energy never change, only the direction does.
SI unit of $B$ : tesla, $1 T = 1 N s C^{- 1} m^{- 1} = 1 N A^{- 1} m^{- 1}$ . Also $1 G = 1 0^{- 4} T$ ; Earth's field is of the order of $1 0^{- 5} T$ .
$v ⊥ B$ : uniform circular motion with $q v B = m v^{2} / r$ , so $r = m v / q B$ . The period $T = 2 π m / q B$ does not depend on $v$ or $r$ .
$v$ at angle $θ$ to $B$ : $v cos θ$ along $B$ is unchanged and $v sin θ$ gives a circle, so the path is a helix with pitch $p = v cos θ \cdot T$ .
Velocity selector: $E$ , $B$ and $v$ mutually perpendicular. Only particles with $v = E / B$ pass undeflected, whatever their charge or mass (used by J.J. Thomson for $e / m$ ).
Direction: for a positive charge use the right-hand rule for $v \times B$ (or Fleming's left-hand rule). For an electron, reverse the answer.

With B into the page a positive charge goes anticlockwise and an electron clockwise. Doubling v doubles r but the period stays the same. — With $B$ into the page a positive charge goes anticlockwise and an electron clockwise. Doubling $v$ doubles $r$ but the period stays the same.

Split v: the part along B (vcostheta) carries the particle forward, the part across B (vsintheta) makes it circle. Pitch uses cos, radius uses sin. — Split $v$ : the part along $B$ ( $v cos θ$ ) carries the particle forward, the part across $B$ ( $v sin θ$ ) makes it circle. Pitch uses cos, radius uses sin.

In crossed fields qE and qvB act in opposite directions. They balance only at v = E/B; faster particles bend one way, slower ones the other. — In crossed fields $q E$ and $q v B$ act in opposite directions. They balance only at $v = E / B$ ; faster particles bend one way, slower ones the other.

Simulation: A charge moving in a magnetic fieldTry it

Formulas

$F = q (E + v \times B)$
Lorentz force
$F = q v B sin θ$
$θ$ = angle between $v$ and $B$
$r = \frac{m v}{q B} = \frac{p}{q B} = \frac{2 m K}{q B}$
Radius for $v ⊥ B$ ; $K$ = kinetic energy
$T = \frac{2 π m}{q B}$
Period, independent of speed
$ν = \frac{q B}{2 π m}, ω = \frac{q B}{m}$
Frequency and angular frequency of revolution
$p = \frac{2 π m v cos θ}{q B}$
Pitch of the helix
$r = \frac{m v sin θ}{q B}$
Radius of the helix
$v = \frac{E}{B}$
Undeflected speed in crossed fields

Tips, tricks and hacks

Radius ratio by what is sameSame

v

r \propto m / q

. Same

p

r \propto 1/ q

. Same

K

r \propto m / q

. Example: proton and

α

with the same

K

1 /1 : 4 /2 = 1 : 1

, equal radii.

Same accelerating voltageAfter falling through

V

K = q V

, so

r = \frac{1}{B} 2 mV / q \propto m / q

. Proton : deuteron :

α

= 1 : 2 : 2

Period ignores speed

T \propto m / q

only. An

α

particle (

m = 4

q = 2

in proton units) takes twice the proton's period at any speed.

Zero work filterAny option saying a magnetic field alone changes speed or kinetic energy is wrong. Example: electron enters

B

1 0^{6}

m/s; it leaves at

1 0^{6}

m/s.

Common mistakes

✗ Magnetic force can speed up or slow down a charge.

✓ $F ⊥ v$ , so work is zero and speed is constant; only an electric field changes speed.

✗ A faster particle in the same field takes longer to go round.

✓ Bigger $v$ gives bigger $r$ in the same ratio, so $T = 2 π m / q B$ is unchanged.

✗ Using $v sin θ$ for the pitch of the helix.

✓ Pitch is distance along $B$ in one period, so it uses $v cos θ$ ; radius uses $v sin θ$ .

✗ Applying the right-hand rule to an electron and keeping the answer.

✓ The rule gives the force on a positive charge; reverse it for negative charges.

NEET traps

A neutron, or any charge moving parallel to $B$ , goes straight undeflected. NEET may call this "no force even though $B \neq = 0$ ": TRUE.

"Kinetic energy of a charge in a uniform magnetic field stays constant" is TRUE, but momentum (a vector) keeps changing.

The velocity selector condition $v = E / B$ does not depend on charge, sign or mass: electrons and protons at that speed both go straight.

Quick check: A proton and an

α

particle enter the same uniform magnetic field perpendicular to it with the same speed. The ratio

r_{α} / r_{p}

of their radii is

Answer: B. $r = m v / q B \propto m / q$ : $(4/2) / (1/1) = 2$ .

Topic 2 · 🔒

Biot-Savart law

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Topic 3 · 🔒

Ampere's circuital law and solenoids

Key points, graphs, every formula, tricks, common mistakes and NEET traps for this topic are inside Dhruv.

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Topic 4 · 🔒

Force and torque on current carrying conductors

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Topic 5 · 🔒

Moving coil galvanometer

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