State Ampere's circuital law. Use this law to find the magnetic field due to a straight infinite current-carrying wire. How are the magnetic field lines different from electrostatic field lines?
Solution
\textbf{Ampere's law:} the line integral of B around any closed loop equals μ0 times the current threading it: ∮B⋅dℓ=μ0I. For an infinite straight wire, take a circular amperian loop of radius r coaxial with the field lines. By symmetry B is constant along it and tangential, so
∮B⋅dℓ=B(2πr)=μ0I⇒B=2πrμ0I.
Magnetic field lines form continuous closed loops (no magnetic monopoles), whereas electrostatic field lines are open, starting on positive and ending on negative charges.
CBSE Class 12 Board · 2016 · All India · Subjective