Doubtclip is an AI tutor that turns any homework or exam doubt into a step-by-step whiteboard video lesson with diagrams, formulas, and voice explanation.

Who is the founder of Doubtclip?

Vinay Malav is the founder of Doubtclip (Founder, Doubtclip, based in Kota, Rajasthan, India). More: https://www.doubtclip.com/about

Which subjects and exams does it support?

It supports Physics, Chemistry, Mathematics/Calculus and related STEM doubts for school boards, JEE, NEET, and global high-school / undergrad practice.

How do I get a video solution?

Upload a photo of the question or paste the text, sign in, and Doubtclip generates a whiteboard-style explanation video you can watch and share.

Is Doubtclip available worldwide?

Yes. Doubtclip is a web app for students globally. Lessons are available in English and Hinglish.

Two long parallel wires carrying currents in the SAME direction will:

Attract each other. Applying the right-hand rule and Lorentz force law F = I(L × B), parallel currents attract, while anti-parallel currents repel.

Physics · Class 12 · JEE / NEET / AP Physics C

Biot-Savart Law & Magnetic Fields

TheBiot-Savart Lawis the magnetostatic equivalent of Coulomb's Law. It calculates the magnetic field $\vec{B}$ generated by any steady current-carrying element $I d\vec{l}$ .

11. Visual Overview & Intuitive Discovery: Biot-Savart Law & Magnetic Fields

In the spring of 1820, Danish professor Hans Christian Ørsted was finishing a lecture on electricity. He happened to have a magnetic compass sitting on his demonstration table near a battery wire. When he connected the wire to complete the circuit, the compass needle twitched and swung 90 degrees. For centuries, electricity and magnetism had been considered two completely separate phenomena. That tiny twitch revealed they are two faces of the exact same force: electromagnetism.

Biot-Savart Law & Current Element Geometry: Biot-Savart Formula, Long Straight Wire, Circular Coil at Center, Axial Field of Loop — Biot-Savart Law & Current Element Geometry
Vector geometry of current element I dl generating magnetic field dB, and axial magnetic field of a circular current loop.
1Biot-Savart Formula — dB = (μ₀/4π) · (I dl × r̂) / r² where μ₀ = 4π × 10⁻⁷ T·m/A
2Long Straight Wire — Field at distance r: B = μ₀ I / (2π r) with concentric circular field lines
3Circular Coil at Center — B = μ₀ N I / (2 R) for a coil with N turns and radius R
4Axial Field of Loop — B = μ₀ I R² / [2(R² + x²)^(3/2)] at distance x along axis

Interactive Study Prompts (Click to Explore)

Clickable

AI Deep Dive 🪄

22. Physical Mechanism Flowchart: Biot-Savart Law & Magnetic Fields

Biot-Savart Law & Magnetic Fields Step-by-Step Flowchart

1
Initial State
Initial parameters and boundary conditions are established.
2
Fundamental Force/Interaction
Governing physical laws act continuously across the system.
3
Energy & Vector Conservation
Conservation principles restrict permitted trajectory states.
4
Dynamic Equilibrium
Final observable state satisfies equilibrium equations.

Follow the numbered pipeline above. In physics examinations, sketching this mental flowchart ensures you never miss intermediate steps in complex multi-concept numericals.

33. Rigorous Mathematical Proofs & Governing Equations

Derivation — Derivation of Governing Formula for Biot-Savart Law & Magnetic Fields

1
$F_{\text{net}} = m a$
Starting from Newton's foundational law
2
$\int F \, dx = \Delta K$
Integrating over displacement

Ampere's Circuital Law

\oint \vec{B} \cdot d\vec{l} = \mu_0 I_{\text{enclosed}}

$I_{\text{enclosed}}$ = Net electric current threading the Amperian loop
$\mu_0$ = Permeability of free space

Core Physical Variables

Variable	Symbol	SI Unit
Energy	E	Joules (J)
Power	P	Watts (W)

Energy
Symbol
E
SI Unit
Joules (J)
Power
Symbol
P
SI Unit
Watts (W)

44. Medical Frontier: Magnetic Resonance Imaging (MRI) Superconducting Coils

Modern hospital MRI scanners create magnetic fields of 3.0 Tesla—60,000 times stronger than Earth's magnetic field. This requires thousands of amperes of current flowing through circular coils. Using the Biot-Savart axial field equation ( $B = \frac{\mu_0 I R^2}{2(R^2+x^2)^{3/2}}$ ), engineers calculate the exact coil geometry needed to produce an ultra-uniform magnetic field at the patient's body, causing hydrogen protons in water molecules to precess and reveal soft tissue tumors without radiation.

Common mistake: Misconception: "A stationary electric charge produces a magnetic field." Static electric charges generate ONLY electrostatic fields. A magnetic field is created strictly by MOVING charges (electric currents) or by time-varying electric fields.

55. Solved Standard & Advanced Exam Problems

Exam question · JEE Standard

Sample Question

Exam question · JEE Advanced / AP Physics C

A circular wire loop of radius R carries a steady current I. At what distance x along the axis of the loop does the magnetic field drop to 1/8 of its value at the center of the loop?

A.x = √3 R
B. $x = 2 R$
C. $x = R / 2$
D. $x = 3 R$

Remember

Magnetic fields are generated by moving charges or electrical currents, not static charges.
Magnetic field lines always form closed continuous loops because isolated magnetic monopoles do not exist.
Field on the axis of a circular current loop decreases as 1/x³ at large distances, resembling a magnetic dipole.

Check yourself

Question 1
Two long parallel wires carrying currents in the SAME direction will: