A long straight wire kept in the horizontal plane carries a current. If the magnetic field produced by the wire at a point 2 m east of the wire is 2 μT in vertically upward direction, the current will be
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 20 A, north to south
A long straight wire produces a field \( B = \mu_0 I/2\pi r \) whose lines are circles around the wire in planes perpendicular to it; the direction follows the right-hand thumb rule.
\( \displaystyle B = \frac{\mu_0 I}{2\pi r} \)
\( \displaystyle I = \frac{2\pi r B}{\mu_0} \)
\( \displaystyle I = \frac{2\pi \times 2\,\mathrm{m} \times 2\times10^{-6}\,\mathrm{T}}{4\pi\times10^{-7}\,\mathrm{T\,m\,A^{-1}}} \)
\( \displaystyle I = 20\,\mathrm{A} \)
For the field at a point due east of the wire to be vertical, the circle of field lines must lie in the vertical east–west plane, so the wire runs north–south.
Point the right thumb towards the south (current from north to south): the fingers curl downwards on the west side of the wire and upwards on the east side. So a current from north to south gives an upward field at the point 2 m east.