Home › UP Board Class 12 › physics › Moving Charges and Magnetism › The magnetic field at a distance $r$ from a LONG…
The magnetic field at a distance $r$ from a LONG STRAIGHT wire carrying current $I$ is
A$\dfrac{\mu_0\,I}{2\pi r}$
B$\dfrac{\mu_0\,I}{4\pi r}$
C$\dfrac{\mu_0\,I}{2 r^2}$
D$\dfrac{\mu_0\,I r}{2\pi}$
Answer & Solution
Correct answer: A. $\dfrac{\mu_0\,I}{2\pi r}$
1. Apply Ampere's law with a circular Amperian loop of radius $r$ centred on the wire.
2. By symmetry, $\vec{B}$ is tangential to the loop with the same magnitude everywhere on it.
3. $\oint\vec{B}\cdot d\vec{l} = B\,(2\pi r) = \mu_0 I$.
4. Solve: $B = \dfrac{\mu_0\,I}{2\pi r}$.
5. Field circles around the wire (right-hand rule: thumb along $I$, fingers curl in the direction of $\vec{B}$).
6. Option B drops a factor of 2. Option C has wrong distance dependence. Option D would grow with $r$.
_Source: NCERT Class 12 Physics Part 1, Ch 4, §4.5 (Ampere's Law applied to a long straight wire), p. 15–16._
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