NDA Physics · Electricity and Magnetism

Magnetism and Magnetic Effects of Current

Magnets and the Earth set up magnetic fields drawn as closed field lines; an electric current does the same — a straight wire makes circular field lines (B ∝ I/r), a solenoid makes a uniform interior field (B = μ₀nI), and a coil concentrates the field at its centre.

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Why this matters

Sixteen PYQs — the chapter's joint-largest subtopic. The bank rewards a handful of facts drilled to reflex: magnetic field lines are closed and never cross, the Earth's field is horizontal at the magnetic equator, which materials a magnet attracts, the field of a straight wire (∝ I/r) and the right-hand grip rule for its direction, the solenoid field B = μ₀nI, and the centre-of-coil field B ∝ NI/R.

Concept 1 of 6: Magnets and magnetic field lines

Every magnet has two poles (north and south) that can't be separated — break a magnet and each piece grows its own pair. We picture the field with lines that leave the north pole, loop around to the south pole OUTSIDE, and continue from south to north INSIDE, forming closed loops that never cross.

Definition

Key facts about a magnet's field lines:

They are closed curves — outside the magnet they run N→S, and they continue S→N inside the magnet (so field lines DO exist within a bar magnet).
They never cross (the field has one definite direction at each point).
They are denser where the field is stronger (near the poles).
A magnetic field is a vector (magnitude and direction).

A bar magnet in a UNIFORM field feels equal and opposite pole forces — so zero net force, only a torque that aligns it.

Field lines are closed curves: outside the magnet they point from N to S; inside they continue from S back to N. They never cross.

Worked example

Can two magnetic field lines ever cross each other? Explain.

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

NDA · Apr 2020 · Q91Moderate

Example 1 · Electricity and Magnetism · Magnetism and Magnetic Effects of Current

Which one of the following statements regarding magnetic field is NOT correct?

Field lines are CLOSED and exist INSIDE the magnet

Two favourite false statements: 'magnetic field lines are open curves' (wrong — they're closed) and 'there are no field lines within a bar magnet' (wrong — they run S→N inside). Both are the answers to 'which is NOT correct'.

Drill 3 more on magnets and magnetic field lines

Concept 2 of 6: The Earth's magnetic field

The Earth behaves like a giant bar magnet tilted slightly from its spin axis. A compass needle dips down at the poles and lies flat at the magnetic equator — that's where the field is purely horizontal.

Definition

The Earth's magnetic field resembles that of a bar magnet at its centre. The angle the field makes with the horizontal is the dip (inclination): it is 90° (vertical) at the magnetic poles and 0° (horizontal) at the magnetic equator. So the Earth's field becomes horizontal at the magnetic equator.

Worked example

Where on Earth does a freely suspended magnetic needle (free to dip) rest exactly horizontal?

Practice this concept3 quick reps

The same idea in a real exam question:

NDA · Apr 2017 · Q53Easy

Example 2 · Electricity and Magnetism · Magnetism and Magnetic Effects of Current

At which place Earth's magnetic field becomes horizontal ?

Magnetic EQUATOR, not magnetic meridian

The field is horizontal at the magnetic equator. 'Magnetic meridian' (the vertical plane containing the needle) and 'geographic pole' are distractors — the equator is where dip = 0.

Concept 3 of 6: Magnetic materials — what a magnet attracts

Only a few materials are strongly attracted to a magnet — iron, nickel, cobalt, and steels containing them. Most everyday materials (plastic, carbon, copper, glass) are not. A handful, like aluminium, are weakly affected.

Definition

Materials fall into three magnetic classes by how they respond to a magnet:

Class	Behaviour	Examples
Ferromagnetic	Strongly attracted; can be magnetised	Iron, nickel, cobalt, steel (incl. many stainless steels)
Paramagnetic	Very weakly attracted	Aluminium, platinum, manganese
Diamagnetic / non-magnetic	Not attracted (very weakly repelled)	Plastic, carbon, copper, glass, water

A magnet strongly attracts only ferromagnetic materials; plastic and carbon are non-magnetic.

Practice this conceptself-check · 3 quick reps

The same idea in a real exam question:

NDA · Sep 2023 · Q135Hard

Example 3 · Electricity and Magnetism · Magnetism and Magnetic Effects of Current

How many of the following materials can be attracted by a magnet? 1. Plastic 2. Carbon 3. Aluminium 4. Stainless Steel Select the correct answer using the code given below:

Stainless steel is (usually) magnetic; aluminium is only weakly so

Common stainless steels contain iron and ARE attracted by a magnet. Aluminium is paramagnetic — weakly attracted, which the bank counts as 'attracted'. Plastic and carbon are not. That gives 2 of the 4.

Concept 4 of 6: Magnetic field of a current-carrying straight wire

A current makes a magnetic field that wraps around the wire in circles. The bigger the current and the closer you are, the stronger the field — it grows with current and falls off as 1/distance. Point your right thumb along the current and your curled fingers show which way the field circles.

Definition

A straight current-carrying wire produces circular magnetic field lines centred on the wire. Its strength is $B = \dfrac{\mu_0 I}{2\pi r}$ — proportional to the current $I$ , inversely proportional to the distance $r$ . It does NOT depend on the wire's own radius. Right-hand grip (thumb) rule: point the right thumb along the conventional current; the curled fingers give the field's circulation direction.

Field of a straight wire

B = \dfrac{\mu_0 I}{2\pi r}

Bmagnetic field (tesla)
Icurrent in the wire (A)
rperpendicular distance from the wire (m)
$\mu_0$ permeability of free space

Field lines circle the wire; point your right thumb along the current (out of the page) and your fingers curl the way the field circulates.

Worked example

At a fixed point near a long straight wire the field is B. If the current is doubled and the point stays put, what is the new field?

Practice this conceptself-check · 3 quick reps

The same idea in a real exam question:

NDA · Apr 2022 · Q67Moderate

Example 4 · Electricity and Magnetism · Magnetism and Magnetic Effects of Current

The magnetic field produced by a current-carrying straight wire at a point outside the wire depends

Depends on current and distance — not on the wire's radius

The field outside a straight wire depends on the current and your distance from the axis, NOT on the wire's own thickness or the surrounding temperature. B ∝ I and B ∝ 1/r.

Drill 3 more on magnetic field of a current-carrying straight wire

Concept 5 of 6: Magnetic field of a solenoid

Wind a wire into a tight coil (a solenoid) and the fields of all the turns add up inside to give a strong, UNIFORM field — just like a bar magnet's. Pack in more turns per metre or push more current and the field grows in proportion. Slip a soft-iron core inside and it grows much more.

Definition

Inside a long solenoid the field is uniform and given by $B = \mu_0 n I$ — proportional to the turns per unit length $n$ and the current $I$ . It does NOT depend on the solenoid's diameter. Inserting a soft-iron core greatly increases the field. A current-carrying solenoid behaves like a bar magnet.

Field inside a solenoid

B = \mu_0 n I

Bfield inside the solenoid (T)
nturns per unit length (per m)
Icurrent (A)

Inside a long solenoid the field is strong and uniform (B = μ₀nI); outside, the loops close like a bar magnet's, with N and S ends.

Worked example

A solenoid carries current I with n turns per unit length, giving a field B. If the turns per unit length are doubled to 2n (current unchanged), what is the new field?

Practice this conceptself-check · 3 quick reps

The same idea in a real exam question:

NDA · Apr 2017 · Q87Easy

Example 5 · Electricity and Magnetism · Magnetism and Magnetic Effects of Current

In a solenoid, the current flowing through the wire is

I

and number of turns per unit length is

n

. This gives a magnetic field

B

inside the solenoid. If number of turn per unit length is increased to

2n

, what will be the value of magnetic field in the solenoid ?

Field depends on turns-per-length and current, not diameter

B = μ₀nI: only n and I matter. A common false statement is 'inserting a soft-iron bar leaves the field unchanged' — wrong, the core boosts it sharply. Another distractor adds the diameter as a dependence — it isn't one.

Drill 4 more on magnetic field of a solenoid

Concept 6 of 6: Magnetic field at the centre of a circular coil

Bend the wire into a circular loop and the field is strongest right at the centre. Stack N turns and the field multiplies by N; shrink the radius and the field grows (it goes as 1/R). So more turns and a smaller loop both intensify the centre field.

Definition

At the centre of a circular coil of $N$ turns, radius $R$ , carrying current $I$ : $B = \dfrac{\mu_0 N I}{2R}$ — proportional to $N$ and $I$ , inversely proportional to $R$ .

Field at centre of a coil

B = \dfrac{\mu_0 N I}{2R}

Nnumber of turns
Icurrent (A)
Rradius of the coil (m)

Worked example

A circular coil produces a field B at its centre. The number of turns is doubled and the radius is halved (current unchanged). What is the new centre field?

Practice this conceptself-check · 3 quick reps

The same idea in a real exam question:

NDA · Sep 2018 · Q122Moderate

Example 6 · Electricity and Magnetism · Magnetism and Magnetic Effects of Current

A circular coil of radius

R

having

N

number of turns carries a steady current

I

. The magnetic induction at the centre of the coil is 0·1 tesla. If the number of turns is doubled and the radius is halved, which one of the following will be the correct value for the magnetic induction at the centre of the coil?

Combine the factors: N up AND R down both raise B

B ∝ N/R. Doubling N gives ×2; halving R gives another ×2; together ×4. Forgetting one factor (answering 0.2 T) is the dominant trap.

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (3)

Magnetic field of a current-carrying straight wire
Field of a straight wire
$B = \dfrac{\mu_0 I}{2\pi r}$
Magnetic field of a solenoid
Field inside a solenoid
$B = \mu_0 n I$
Magnetic field at the centre of a circular coil
Field at centre of a coil
$B = \dfrac{\mu_0 N I}{2R}$

Reference tables (1)

Magnetic materials — what a magnet attracts3 rows

Class	Behaviour	Examples
Ferromagnetic	Strongly attracted; can be magnetised	Iron, nickel, cobalt, steel (incl. many stainless steels)
Paramagnetic	Very weakly attracted	Aluminium, platinum, manganese
Diamagnetic / non-magnetic	Not attracted (very weakly repelled)	Plastic, carbon, copper, glass, water

A magnet strongly attracts only ferromagnetic materials; plastic and carbon are non-magnetic.

Watch out for (6)

Field lines are CLOSED and exist INSIDE the magnet
→ Magnets and magnetic field lines
Magnetic EQUATOR, not magnetic meridian
→ The Earth's magnetic field
Stainless steel is (usually) magnetic; aluminium is only weakly so
→ Magnetic materials — what a magnet attracts
Depends on current and distance — not on the wire's radius
→ Magnetic field of a current-carrying straight wire
Field depends on turns-per-length and current, not diameter
→ Magnetic field of a solenoid
Combine the factors: N up AND R down both raise B
→ Magnetic field at the centre of a circular coil

Test yourself on Electricity and Magnetism

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