Question

A straight conductor carrying a current $I$ splits into two identical semicircular arcs as shown in figure below. What is the magnitude of the magnetic field at the center $C$ of the resulting circular arcs of radius $R$?

• A. $0$
• B. $\frac{{\mu }_{0}l}{4R}$
• C. $\frac{{\mu }_{0}l}{2R}$
• D. $\frac{{\mu }_{0}l}{R}$

Answer 1

Answer: (A)

Magnetic field due to BAC arc is
$B=\frac{{\mu }_0\pi (I/2)}{4\pi R}\otimes$ ... (i)
Magnetic field due to $ADC$ are is
$B=\frac{{\mu }_0\pi (I/2)}{4\pi R}$ ... (ii) F
rom Eqs. (i) and (ii) n
et magnetic field is zero.