Magnetic Effects of Current and Magnetism Formula Sheet — JEE Main Physics

Q: What are the most important Magnetic Effects of Current and Magnetism formulas for JEE Main?

This Magnetic Effects of Current and Magnetism formula sheet covers all the high-yield Physics formulas, definitions and theorems you need for JEE Main, across Biot-Savart law, Application to current carrying circular loop, Ampere's law, Applications to infinitely long straight wire and solenoid, Force on moving charge in magnetic and electric fields — each shown with the key result and, where useful, a worked example.

Q: Is this Magnetic Effects of Current and Magnetism formula sheet free?

Yes — the full chapter formula sheet is free to read online, no login or payment required.

Q: How should I revise Magnetic Effects of Current and Magnetism formulas?

Blurt the Magnetic Effects of Current and Magnetism formulas from memory, then check against this sheet to find your gaps — and practise a few previous-year questions on the chapter to make sure you can apply them under time pressure.

Every key Magnetic Effects of Current and Magnetism formula, definition and theorem for JEE Main Physics in one place — with common examiner traps and worked examples. Free to read; blurt from memory, then check your gaps.

Syllabus — topics coveredNTA · 18 sub-topics

Biot-Savart law
Application to current carrying circular loop
Ampere's law
Applications to infinitely long straight wire and solenoid
Force on moving charge in magnetic and electric fields
Force on current-carrying conductor
Force between parallel current carrying conductors
Definition of ampere
Torque on current loop in magnetic field
Moving coil galvanometer
Conversion to ammeter and voltmeter
Current loop as magnetic dipole
Bar magnet as equivalent solenoid
Magnetic field lines
Magnetic field due to magnetic dipole
Torque on magnetic dipole
Para-, dia- and ferromagnetic substances
Effect of temperature on magnetic properties

Magnetic Force on a Moving Charge

Lorentz force

F = q (v \times B); F = q (E + v \times B)

q =

charge,

v =

velocity,

B =

field; magnetic part

⊥ v \Rightarrow

does NO work

Circular motion (

v ⊥ B

)

r = \frac{m v}{qB} = \frac{2 m K}{qB}; T = \frac{2 πm}{qB}; f = \frac{qB}{2 πm}

T,f (cyclotron) are

independent of speed

and radius

A positive charge moving in a magnetic field into the page follows a circular path with the magnetic force pointing to the centre — Force is centripetal; the charge circles.

Comparative: orientation of

v

B

$v$ vs $B$	Path	Force
parallel	straight line	$0$
perpendicular	circle, $r = m v / qB$	$q v B$ (centripetal)
at angle $θ$	helix	$qvB sin θ$

Helical motion

r = \frac{m v sin θ}{qB}; pitch = \frac{2 πm v cos θ}{qB}

pitch

=

axial advance per revolution

⚡ Shortcut · Velocity selector & cyclotron

Crossed

E, B

: undeflected when

v = E / B

. Cyclotron exit energy

K = \frac{q ^{2} B ^{2} R ^{2}}{2 m}

(independent of the gap voltage).

🚫 Examiner Trap · Magnetic force on a charge

(1) Magnetic force is

⊥ v

, so it does

zero work

— speed and KE never change, only direction. (2)

T = 2 πm / qB

independent of speed

— faster charges just take bigger circles. (3) A charge at rest, or moving

∥ B

, feels NO magnetic force. (4) The pitch uses

v cos θ

, the radius uses

v sin θ

— don't swap.

Force on a Current-Carrying Conductor

Force on a conductor

F = I (L \times B); F = BIL sin θ

I =

current,

L =

length,

θ =

angle between

L

and

B

; element

d F = I d l \times B

Two parallel wires carrying currents in the same direction attract each other — Parallel currents attract; antiparallel repel.

Force between parallel wires

\frac{F}{l} = \frac{μ _{0} I _{1} I _{2}}{2 π d}

d =

separation; same direction

\to

attract, opposite

\to

repel

Field of a moving charge

B = \frac{μ _{0}}{4 π} \frac{q ( v \times r ^ )}{r ^{2}}

\overset{r}{^} =

unit vector from charge to field point

⚡ Shortcut · Definition of the ampere

1

=

the current which, in two infinite parallel wires

1

m apart, gives a force of

2 \times 1 0^{- 7}

N/m. (This fixes

μ_{0} = 4 π \times 1 0^{- 7}

🚫 Examiner Trap · Force on conductors

(1) Parallel currents

attract

, antiparallel

repel

— the OPPOSITE of like/unlike charges. (2)

F = BIL sin θ

: a wire

∥ B

feels NO force. (3) Force is on the wire as a whole via

L \times B

— use the direction of I. (4) The field a current makes does not exert a force on its own wire.

Biot-Savart Law & Magnetic Fields

Biot-Savart law

d B = \frac{μ _{0}}{4 π} \frac{I d l \times r ^}{r ^{2}}

\frac{μ _{0}}{4 π} = 1 0^{- 7}

T m/A; direction by right-hand rule

Comparative: field of standard shapes

Geometry	$B$
Finite wire	$\frac{μ _{0} I}{4 π d} (sin θ_{1} + sin θ_{2})$
Infinite wire	$\frac{μ _{0} I}{2 π d}$
Arc (angle $ϕ$ rad)	$\frac{μ _{0} I ϕ}{4 π R}$
Semicircle	$\frac{μ _{0} I}{4 R}$
Loop centre	$\frac{μ _{0} N I}{2 R}$

Concentric circular magnetic field lines around a long straight current-carrying wire — Field circles the wire (RH grip rule).

Circular loop (

N

turns), on axis

B_{a x i s} = \frac{μ _{0} N I R ^{2}}{2 ( x ^{2} + R ^{2} ) ^{3/2}}

R =

loop radius,

x =

axial distance; centre

x = 0 \Rightarrow B = μ_{0} N I /2 R

Magnetic field on the axis of a circular current loop pointing along the axis — On-axis field of a current loop.

🚫 Examiner Trap · Biot-Savart & fields

(1) A straight segment

aimed at

the point (

d l ∥ \overset{r}{^}

) gives

zero

field. (2) Arc angle

ϕ

must be in

radians

. (3) Finite wire uses

sin θ_{1} + sin θ_{2}

(angles from the foot of perpendicular) — for a semi-infinite wire one term is

sin 9 0^{\circ} = 1

. (4)

B \propto 1/ d

for a wire but

\propto 1/ x^{3}

far on a loop's axis.

Ampere's Circuital Law

Ampere's circuital law

\oint B \cdot d l = μ_{0} I_{e n c}

I_{e n c} =

current threading the Amperian loop; use only with high symmetry

Comparative: solid wire (radius

R

, uniform

I

)

Region	$B$
Inside ( $r < R$ )	$\frac{μ _{0} I r}{2 π R ^{2}}$ ( $\propto r$ )
Outside ( $r > R$ )	$\frac{μ _{0} I}{2 π r}$ ( $\propto 1/ r$ )
Hollow pipe, inside	$0$

A solenoid with a uniform magnetic field along its axis inside — Solenoid: uniform field inside.

Solenoid / toroid

B_{so l} = μ_{0} n I (ends \frac{1}{2} μ_{0} n I); B_{t or} = \frac{μ _{0} N I}{2 π r}

n = N / L =

turns per unit length

🚫 Examiner Trap · Ampere's law

(1) Works only for

symmetric

fields (infinite wire/sheet/solenoid/toroid) — otherwise

B

can't be pulled out of the integral. (2) Field at a solenoid

end

is HALF the inside value (

\frac{1}{2} μ_{0} n I

). (3) Field is uniform

inside

a long solenoid,

\approx 0

outside. (4) Inside a hollow current-carrying pipe

B = 0

(

I_{e n c} = 0

Magnetic Dipole, Torque & Galvanometer

Magnetic moment & torque

m = N I A; τ = m \times B (τ = NIAB sin θ); U = - m \cdot B

θ =

angle between

m

and

B

; stable at

θ = 0

τ

max at

θ = 9 0^{\circ}

A current loop in a uniform field experiences a torque that tends to align its magnetic moment with the field — Torque aligns $m$ with $B$ .

Moving-coil galvanometer

NIAB = Cθ \Rightarrow I = \frac{C}{N A B} θ

C =

torsional constant; current sensitivity

\frac{N A B}{C}

, voltage sensitivity

\frac{N A B}{CR}

Comparative: ammeter vs voltmeter

	Ammeter	Voltmeter
Connection	series	parallel
Resistance	low ( $0$ ideal)	high ( $\infty$ ideal)
From G via	shunt $S = \frac{G i _{g}}{I - i _{g}}$	series $R = \frac{V}{i _{g}} - G$

🚫 Examiner Trap · Dipole, torque & galvanometer

(1) Torque is

max at θ = 9 0^{\circ}

⊥

B),

zero at θ = 0

— opposite to many guesses. (2) A uniform field gives torque but

no net force

. (3) The galvanometer's

radial

field makes

τ \propto I

(linear scale) and keeps

sin θ = 1

. (4) Increasing N raises sensitivity but also resistance.

Bar Magnet & Earth's Magnetism

Bar magnet

▸Behaves like a solenoid / magnetic dipole; magnetic poles exist $only in pairs$ (no monopole).
▸Magnetic moment $M = m (2 l)$ (pole strength $\times$ length); points S $\to$ N inside.

Field of a short bar magnet

B_{a x ia l} = \frac{μ _{0}}{4 π} \frac{2 M}{d ^{3}}; B_{e q u a t or ia l} = \frac{μ _{0}}{4 π} \frac{M}{d ^{3}}

d =

distance from centre;

B_{a x ia l} : B_{e q u a t or ia l} = 2 : 1

Field lines of a bar magnet emerging from the north pole and entering the south pole — Field lines run N → S outside, S → N inside.

Magnetisation

B = μ_{0} (H + M) = μ_{0} μ_{r} H; χ = \frac{M}{H}, μ_{r} = 1 + χ

M =

moment per unit volume,

H =

magnetising field,

χ =

susceptibility (dimensionless)

Earth's magnetic elements

B_{H} = B cos δ, B_{V} = B sin δ, tan δ = \frac{B _{V}}{B _{H}}

δ =

dip/inclination; declination

=

angle between magnetic & geographic meridians

🚫 Examiner Trap · Bar magnet & earth's field

(1) Axial field is

twice

the equatorial at the same distance; both fall as

1/ d^{3}

. (2) Dip

δ = 0^{\circ}

at the magnetic

equator

9 0^{\circ}

at the poles (

B_{H}

max at equator). (3) Breaking a magnet gives two smaller magnets — never an isolated pole. (4) Inside the magnet field runs S

\to

N (opposite to outside).

Magnetic Materials

Comparative: dia / para / ferro

Property	Dia	Para	Ferro
$χ$	small $-$ ve	small $+$ ve	large $+$ ve
$μ_{r}$	$< 1$	$≳ 1$	$≫ 1$
In a field	weakly repelled	weakly attracted	strongly attracted
With $T ↑$	independent	$χ = C / T$ falls	ferro $\to$ para at $T_{c}$
Example	Bi, Cu, $H_{2}$ O	Al, Na, $O_{2}$	Fe, Co, Ni

Curie law

χ = \frac{C}{T} (paramagnetic)

ferromagnetic

\to

paramagnetic above the Curie temperature

T_{c}

B-H hysteresis loop of a ferromagnet showing retentivity and coercivity — Hysteresis: B lags H; loop area $=$ energy lost/cycle.

Reading the loop

▸ $Retentivity$ : residual B at $H = 0$ ; $coercivity$ : reverse H needed to make $B = 0$ .
▸ $Soft iron$ (narrow loop, low coercivity) $\to$ transformers, electromagnets.
▸ $Steel$ (wide loop, high coercivity) $\to$ permanent magnets.

🚫 Examiner Trap · Magnetic materials

(1) Diamagnetism is

universal

but weak; it shows only when there's no para/ferro to mask it.

χ_{d ia}

is T-independent. (2) Curie law

χ = C / T

is for

paramagnetics

— susceptibility FALLS as T rises. (3) Choose the material by loop:

soft

for cores (low loss),

hard

for permanent magnets. (4) Above

T_{c}

a ferromagnet becomes paramagnetic.

More JEE Main Physics formula sheets

Frequently Asked Questions

What are the most important Magnetic Effects of Current and Magnetism formulas for JEE Main?

This Magnetic Effects of Current and Magnetism formula sheet covers all the high-yield Physics formulas, definitions and theorems you need for JEE Main, across Biot-Savart law, Application to current carrying circular loop, Ampere's law, Applications to infinitely long straight wire and solenoid, Force on moving charge in magnetic and electric fields — each shown with the key result and, where useful, a worked example.

Is this Magnetic Effects of Current and Magnetism formula sheet free?

Yes — the full chapter formula sheet is free to read online, no login or payment required.

How should I revise Magnetic Effects of Current and Magnetism formulas?

Blurt the Magnetic Effects of Current and Magnetism formulas from memory, then check against this sheet to find your gaps — and practise a few previous-year questions on the chapter to make sure you can apply them under time pressure.

Also useful: all formula sheets · JEE Main previous-year papers · most important chapters.