Two long straight parallel wires are 10 cm apart. They carry currents of 4 A and 6 A in opposite directions. The magnitude of the magnetic field at the point midway between the wires is (take \(\mu_0=4\pi\times10^{-7}\ \mathrm{T\,m\,A^{-1}}\))
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(4.0\times10^{-5}\ \mathrm{T}\)
A long straight wire gives a field \(B=\mu_0I/2\pi r\) at a distance \(r\). The midpoint is 5 cm from each wire. By the right-hand rule, two currents in opposite directions give fields in the same direction at any point between the wires. So the two fields add.
Distance from each wire, \(r=5\ \mathrm{cm}=0.05\ \mathrm{m}\)
\( \begin{aligned} B_1 &= \frac{\mu_0 I_1}{2\pi r} \\ &= \frac{4\pi\times10^{-7}\times4}{2\pi\times0.05} \\ &= 1.6\times10^{-5}\ \mathrm{T} \end{aligned} \)
\( \begin{aligned} B_2 &= \frac{\mu_0 I_2}{2\pi r} \\ &= \frac{4\pi\times10^{-7}\times6}{2\pi\times0.05} \\ &= 2.4\times10^{-5}\ \mathrm{T} \end{aligned} \)
\( \begin{aligned} B &= B_1+B_2 \\ &= 1.6\times10^{-5}+2.4\times10^{-5} \\ &= 4.0\times10^{-5}\ \mathrm{T} \end{aligned} \)
NCERT (2026-27):
Summary – “7. The magnitude of the magnetic field at a distance R from a long, straight wire carrying a current I is given by:”
\( B=\frac{\mu_0 I}{2\pi R} \)
Ampere’s Circuital Law – “… Grasp the wire in your right hand with your extended thumb pointing in the direction of the current. Your fingers will curl around in the direction of the magnetic field.”