Physics · Moving Charges And Magnetism · NEET
I dl is a VECTOR. The current I is a scalar, but dl (the small length) points along the direction the current flows, so the product I dl is a vector. This is the exact point NEET 2022 tested: charge q in Coulomb's law is a scalar source, but the current element I dl in Biot-Savart law is a vector source. Do not swap them.
Because dB comes from the cross product dl × r̂, and a cross product uses the sine of the angle between the two vectors. So dB = (μ₀/4π)(I dl sinθ)/r². When dl points straight at your point (θ = 0° or 180°), sinθ = 0, so that element gives ZERO field on its own axis. Field is maximum when dl is perpendicular to r (θ = 90°, sinθ = 1).
dB is along dl × r̂ (the cross product). Use the right-hand rule: point your fingers along the current element dl, curl them toward the line r pointing to your target point, and your thumb gives dB. For a straight wire this means the field circles around the wire — into the page on one side, out of the page on the other.
No. It only gives dB from ONE infinitesimal element I dl. To get the total field B of a full wire or loop, you must add up (integrate) every element: B = ∫ dB. This is why the law alone gives just a piece — you integrate over the whole conductor for the real answer.
μ₀ = 4π × 10⁻⁷ T·m/A, so μ₀/4π = 10⁻⁷ T·m/A exactly. Memorise this — it lets you plug numbers in fast during NEET calculations. It plays the same role that 1/4πε₀ = 9 × 10⁹ plays in Coulomb's law.
Two statements are given. Statement I: Biot-Savart's law gives the magnetic field of an infinitesimal current element (I dl) of a current-carrying conductor only. Statement II: Biot-Savart's law is analogous to Coulomb's inverse-square law, with the former being the field produced by a scalar source I dl, while the latter is produced by a vector source q. Choose the most appropriate answer.
Try the real previous-year questions from this chapter — each with the answer and a full solution.
The magnetic field dB from a small current element I dl at a point distance r away is dB = (μ₀/4π)(I dl sinθ)/r², directed along dl × r̂.
μ₀ is the permeability of free space, μ₀ = 4π × 10⁻⁷ T·m/A (tesla metre per ampere). Its combination μ₀/4π = 10⁻⁷ T·m/A.
Both are long-range and depend on 1/r² (inverse square of distance), and the principle of superposition applies to both. The key difference: Biot-Savart's source is a vector current element I dl and its field is a cross product, while Coulomb's source is a scalar charge q with a field along the line joining them.
When θ = 0° or 180°, i.e. along the line of the current element itself, sinθ = 0, so dB = 0. The field is strongest at θ = 90° (perpendicular).
It is the starting formula used to derive the field of a straight wire, a circular loop, an arc, and a solenoid. Statement-based and formula questions on it appear directly (like NEET 2022), and every field-derivation question depends on it.
