Home › ISC Class 12 › Physics › Moving Charges and Magnetism › A long straight wire of circular cross-section (…
A long straight wire of circular cross-section (radius a) carries a uniformly distributed steady current I. For a point inside the wire at distance r < a, the magnetic field varies as:
AB ∝ r
BB ∝ 1/r
CB ∝ 1/r²
DB ∝ r²
Answer & Solution
Correct answer: A. B ∝ r
1. For $r < a$, the enclosed current is the fraction in area $\pi r^2$: $I_e = I\dfrac{r^2}{a^2}$.
2. Ampère's law: $B(2\pi r) = \mu_0 I_e = \mu_0 I\dfrac{r^2}{a^2}$.
3. Solve: $B = \dfrac{\mu_0 I}{2\pi a^2}\,r$.
4. With $a$ fixed, $B \propto r$ (the $1/r$ behaviour applies only outside, for $r > a$).
_Source: NCERT Class 12 Physics Ch 4 "Moving Charges and Magnetism", p.151_
Related questions
An electron and a proton enter a magnetic field with the same kinetic energy, perpendiculaA galvanometer is converted into an ammeter of higher range by connecting:The work done by a static magnetic force on a moving charge is:Magnetic field at a point on the axis of a circular loop, far from the loop (distance x ≫ The dimensional formula of the magnetic field B (in SI units of tesla) is:A cyclotron of magnetic field B accelerates positive charges of mass m, charge q. The cyclTorque on a magnetic dipole (current loop) of moment m placed in a uniform field B at anglTwo long parallel wires carry currents I₁ and I₂ in the SAME direction, separated by dista