A straight current-carrying wire carrying current \(I\) passes perpendicular to the plane of an imaginary rectangular loop PQRS, passing through its centre O (into the diagram). The diagonals intersect at \(60^\circ,\) and side PS is smaller than side PQ. The value of \(\int \vec{B} \cdot \overrightarrow{dl}\) evaluated from P to Q (along PQ) has the magnitude:
               
\(1.~ \frac{\mu_{0} I}{6}\\ 2.~ \frac{2 \mu_{0} I}{6}\\ 3.~ \frac{4\mu_{0} I}{6}\\ 4.~\frac{5\mu_{0} I}{6}\)
Subtopic:  Ampere Circuital Law |
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From Ampere's circuital law, for a long straight wire of circular cross-section carrying a steady current, the variation of the magnetic field inside and outside the region of the wire is:
1. a linearly decreasing function of distance upto the boundary of the wire and then a linearly increasing one for the outside region.
2. uniform and remains constant for both regions.
3. a linearly increasing function of distance upto the boundary of the wire and then a linearly decreasing one for the outside region.
4. a linearly increasing function of distance \(r\) upto the boundary of the wire and then decreasing one with \(1/r\) dependence for the outside region.
Subtopic:  Ampere Circuital Law |
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