Topic 3 of 8 • Chapter: Magnetic Effect of Current • Physics

Magnetic Field Due to a Straight Wire – Complete Notes, Revision, Important Questions & Downloads

Magnetic Field Due to a Straight Wire packages General Formula and Special Cases into one usable family: finite wire, infinite wire, semi-infinite wire, axial point, and field inside or outside cylindrical conductors. NEET tests this topic through direct substitution in the standard formula, deciding the correct limiting case, and comparing field variation inside solid or hollow conductors. For example, once a long wire is treated as effectively infinite, the field varies directly with current and inversely with perpendicular distance, so doubling the distance halves the field.

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Direct FormulaeHigh ROINEET Core

Expected QuestionsQ

1-2

questions from long-wire limits and cylindrical conductor cases

Time Required⏱

2.5 Hours

to fix the special cases and the inside-outside behaviour

Difficulty⚡

Medium

standard results are simple, but students often choose the wrong geometric case

NRI USA Curriculum GapUS

Low

long-wire field is usually covered, but inside-cylinder current-distribution cases may be less emphasised

1Subtopics

32+Practice Questions

4Free Downloads

2.5 hrsPrep Time

⬇ Get Free Downloads

NEET Weightage & Exam Pattern

Magnetic Effect of Current

NEET Year	Questions from this Topic	Bar	Marks
2024	1	1 Q	4
2023	2	2 Qs	8
2022	1	1 Q	4
2021	1	1 Q	4
2020	2	2 Qs	8
Topic Weightage	7		28

The infinite straight-wire result B = mu0 I divided by 2 pi r is one of the fastest one-step marks in this chapter.
NEET also checks whether the student can recognise when the semi-infinite or axial-position case should replace the infinite-wire formula.
Uniform current distribution inside solid and hollow cylinders is a common extension that tests Ampere-law reasoning instead of rote substitution.

📊

1.2

Avg Questions / Year

🎯

Total Marks (6 yrs)

📈

Direct

Pattern

⚠️

Medium

Difficulty

Preparation Strategy

Identify the Wire Geometry First Before writing any formula, decide whether the conductor is finite, effectively infinite, semi-infinite, or a cylindrical current distribution. Most mistakes happen before algebra starts because the wrong case is chosen.

Track the Perpendicular Distance The field depends on the shortest perpendicular distance from the point to the wire, not simply on any labelled length in the figure. In NEET diagrams, mixing the actual perpendicular with some oblique segment is a standard trap.

Separate Inside and Outside Cylinder Results Outside a wire or cylinder, the field behaves like that of a long straight conductor carrying the total current. Inside a solid conductor, the enclosed current changes with radius; inside a hollow cylinder, the field can be zero in the hollow part.

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PDF · Cheat Sheet · MCQ Set · PYQ

📄

Full Topic Notes

Notes covering finite, infinite, and semi-infinite wires plus solid and hollow cylindrical conductors.

PDF8 Pages

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📝

Formula Sheet

Special-case sheet listing finite-wire angle form, infinite-wire result, and inside-cylinder formulae.

PDF1 Page

Download Formulas

🎯

MCQ Practice

Practice set on distance dependence, field comparison at different radii, and conductor cross-section cases.

PDF32 Questions

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⏳

Previous Year Questions

Exam-style sheet focused on long straight wires, magnitude comparison, and field inside conductors.

PDF13 Questions

Download PYQs

Topic Coverage

2-Column Table

Column A	Column B
General Formula and Special Cases↗

Quick Revision

Concept → Trap → Example

1) General Formula and Special Cases

Wire Results

For a straight wire, the general field uses the angle form with the two end angles. It reduces to the infinite-wire result mu0 I divided by 2 pi r, the semi-infinite result mu0 I divided by 4 pi r, and zero at an axial point.

Use the full angle-based formula when the wire is finite and the observation point sees different end angles.
For a very long wire near its middle, both end angles become ninety degrees and the standard infinite-wire result follows immediately.
Trap: applying the infinite-wire formula to an end-point geometry where one of the limiting angles is actually zero.

Example (NEET-style)If a current of 10 A flows through a long straight wire and the point is 0.05 m away, the field is proportional to 10 divided by 0.05, so doubling the distance to 0.10 m cuts the field to half.

US Curriculum Gaps

Note for NRI/OCI students studying abroad.

Finite-Wire Angle Form

Many school courses emphasise only the infinite-wire limit, whereas NEET can still test the finite-wire angle expression and ask students to identify the correct limiting geometry.

reading end angles correctly
reducing the finite result to infinite or semi-infinite cases

Current Distribution Inside Conductors

Questions on solid, hollow, and thick hollow cylinders require enclosed-current reasoning that is often skipped in lighter introductory treatments.

uniform current density assumption
field zero in the hollow region

Concept IQ Check

Exam-style checks

1A point is at perpendicular distance r from a long straight wire carrying current I. If the distance is made 4r while current stays unchanged, what happens to the magnetic field?Distance scaling

It becomes four times.

It becomes one-fourth.

It becomes one-sixteenth.

It stays the same.

For an effectively infinite straight wire, the magnetic field varies inversely with the perpendicular distance r. Therefore increasing the distance from r to 4r reduces the field by the same factor 4. The one-sixteenth option comes from confusing this result with an inverse-square law. NEET uses this mistake often because students carry over the distance dependence from other field laws without checking the correct geometry.

2Inside the hollow region of a hollow cylindrical conductor carrying current uniformly in its material, the magnetic field is:Cylinder case

maximum

non-zero and constant

zero

inversely proportional to radius

Within the hollow region, an Amperian loop encloses no current, so the enclosed-current term is zero. That makes the magnetic field zero there. The field becomes non-zero only where current-carrying material is actually enclosed or outside the cylinder where the whole current is enclosed. This is a direct application of Ampere's Law and a common extension of straight-wire field questions in NEET practice.

NEET Practice Questions

Click "Reveal Answer" after attempting

1A long straight wire carries 20 A current. If a point is 0.1 m away from the wire, the magnetic field magnitude is proportional to:

20 divided by 0.1

20 times 0.1

0.1 divided by 20

1 divided by 20 times 0.1

👁 Reveal Answer

20 divided by 0.1. For a long straight wire, the magnetic field magnitude is directly proportional to current and inversely proportional to perpendicular distance. Therefore the proportional part is I over r, which here is 20 divided by 0.1. The other options represent common confusions between direct and inverse dependence on distance.

2For a semi-infinite straight wire, the magnetic field at a point near the end is:

mu0 I divided by 2 pi r

mu0 I divided by 4 pi r

mu0 I divided by pi r

zero

👁 Reveal Answer

Mu0 I divided by 4 pi r. In the semi-infinite case one end angle is ninety degrees and the other is zero, so only one sine term contributes in the general straight-wire expression. That leaves exactly half of the infinite-wire result. Students who write mu0 I divided by 2 pi r are treating the wire as infinite on both sides of the observation point, which is not the geometry described here.

3At a point lying on the axial line of a straight current-carrying conductor, the magnetic field is:

maximum

mu0 I divided by 2 pi r

zero

dependent only on current density

👁 Reveal Answer

Zero. When the observation point lies on the axial position of the wire, the geometry makes the magnetic field contribution vanish because the relevant angular factor collapses. The textbook states this special case separately because it is easy to overlook when students try to apply the standard perpendicular-distance result everywhere.

4Inside a solid cylindrical conductor of radius R carrying uniform current I, the magnetic field at radius r inside the conductor is:

directly proportional to r

inversely proportional to r

independent of r

always zero

👁 Reveal Answer

Directly proportional to r. For uniform current density, the enclosed current inside radius r scales as r squared, and Ampere's Law then gives B proportional to enclosed current divided by r. One factor of r remains, so the field rises linearly from the axis to the surface. This is why the inside-solid-cylinder graph does not have the same 1 over r behaviour as the outside region.

Physics Revision Checklist

Check off chapters as you revise

Use this section for quick chapter tracking before mocks, part tests, and final NEET revision.

General Formula and Special Cases: Learn the End-Angle FormWrite the finite-wire formula and reduce it yourself to the infinite and semi-infinite limits.

General Formula and Special Cases: Mark the Perpendicular DistanceIn every diagram, identify the true perpendicular distance r before doing any substitution.

General Formula and Special Cases: Revise the Axial Position CaseRemember that the field is zero on the axial line of the wire and do not use the long-wire result there.

General Formula and Special Cases: Separate Solid and Hollow CylindersKnow where the field is zero, where it rises with radius, and where it behaves like the outside long-wire result.

General Formula and Special Cases: Practise Enclosed-Current LogicFor conductor cross sections, compute the enclosed current first and only then apply Ampere's Law.

Frequently Asked Questions

Notes · Downloads · Revision · Important Questions

What is the safest formula to start with for a straight wire?

Start with the general finite-wire angle form if the ends matter in the geometry. Then reduce it to the infinite or semi-infinite limit only when the end angles justify that simplification.

Why does the field of a long straight wire vary as 1 over r and not 1 over r squared?

Because after integrating the Biot-Savart contributions of all current elements along the wire, the dependence changes from the current-element form to the long-wire result. The full geometry of the conductor matters.

How do I know a wire can be treated as infinite?

When the observation point is near the middle of a wire that is very long compared with the perpendicular distance, both end angles effectively become ninety degrees and the infinite-wire result is an excellent approximation.

Why is the field zero inside the hollow part of a hollow cylinder?

An Amperian loop drawn in the hollow region encloses no current. Since the enclosed current is zero, the magnetic field there is also zero.

What changes inside a solid cylindrical conductor?

Inside a solid conductor with uniform current density, the enclosed current grows with radius. That makes the magnetic field increase linearly with the distance from the axis until the surface is reached.

What happens to the field outside any cylindrical conductor carrying total current I?

Outside the conductor, the entire current is enclosed, so the field behaves like that of a long straight wire and varies as mu0 I divided by 2 pi r.

Why is the axial-position case separated in the textbook?

Because students often try to force the standard perpendicular-distance formula onto that geometry. On the axis of the conductor, the correct result is zero, so it must be recognised as a distinct special case.

What is the most common exam trap in this topic?

Using the infinite-wire result in every question without first checking whether the wire is finite, semi-infinite, on-axis, or part of a solid or hollow cylinder.

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Magnetic Field Due to a Straight Wire

Magnetic Field Due to a Straight Wire – Complete Notes, Revision, Important Questions & Downloads

1) General Formula and Special Cases

Finite-Wire Angle Form

Current Distribution Inside Conductors

Physics Revision Checklist

NEET NRI Counseling & Admission eBook Download

Schedule Trial Session For NEET Prep

General Formula and Special Cases

Subtopics

General Formula and Special Cases

NEET > Physics > Magnetic Effects of Current and Magnetism Chapters

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Magnetic Field Due to a Straight Wire

Overview content

Magnetic Field Due to a Straight Wire – Complete Notes, Revision, Important Questions & Downloads

1) General Formula and Special Cases

Finite-Wire Angle Form

Current Distribution Inside Conductors

Physics Revision Checklist

NEET NRI Counseling & Admission eBook Download

Schedule Trial Session For NEET Prep

General Formula and Special Cases

Subtopics

General Formula and Special Cases

NEET > Physics > Magnetic Effects of Current and Magnetism Chapters

Comments

Leave a comment

Comments (0)