Physics · Moving Charges And Magnetism · NEET
Yes. Coulomb's law: E = (1/4*pi*e0) * q/r^2. Biot-Savart law: dB = (mu0/4*pi) * I dl sin(theta)/r^2. Both have the 1/r^2 factor, both have a constant made of 1/4*pi, and both are linear in their source (charge q, or current element I dl). So the distance dependence is identical. This is why NEET pairs them: if you know one, the r^2 part of the other is free.
The source decides it. Coulomb's source is a scalar charge q, so the electric field has only one natural direction: along the line joining charge to point (the vector r-hat). No cross product is possible. Biot-Savart's source is a current element I dl, which is a vector (it has a direction of flow). Now two vectors exist: dl and r. Their cross product dl x r gives a field that is perpendicular to both. That is why B curls around a wire instead of pointing away from it.
No. The electric field of a point charge is central: it points radially, straight along r. The magnetic field of a current element is NOT central; it is sideways (perpendicular to r), so it wraps around the wire in circles. A compass near a wire points tangent to a circle, not toward the wire. This is the single most important direction difference for NEET.
The current element I dl plays the role that charge q plays in Coulomb's law. Just as E is proportional to q, dB is proportional to I dl. But note two extras in Biot-Savart: there is no isolated current element in real life (current always flows in a closed loop, unlike a lone charge), and dB also depends on the angle theta between dl and r through sin(theta).
Try the real previous-year questions from this chapter — each with the answer and a full solution.
Both are inverse-square laws (field proportional to 1/r^2), both are linear in the source, both obey superposition (add up the contributions of many sources), and both have a 1/4*pi constant. The distance behaviour is exactly the same.
Coulomb's law gives a central field (E along r) from a scalar charge. Biot-Savart law gives a field perpendicular to dl and r (from the cross product dl x r) produced by a vector current element, and it also depends on the angle theta through sin(theta).
Yes. dB has a sin(theta) factor, where theta is the angle between dl and r. So dB is maximum when dl is perpendicular to r (sin 90 = 1) and zero when dl is along r (sin 0 = 0). Coulomb's law has no such angle factor for a point charge because a scalar charge has no direction.
No. A single point charge can exist alone, but a current element I dl cannot exist by itself; current always flows in a complete closed circuit. So Biot-Savart law is a rule for one piece that must be integrated over the whole loop to get a real, measurable field.
It lets you transfer intuition: the 1/r^2 and superposition ideas carry straight over from electrostatics, so you only need to add the cross-product (direction) and sin(theta) (angle) rules to master magnetic fields. It also blocks the common trap of pointing B radially outward.
