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A long straight wire of circular cross-section (radius a) is carrying steady current I. The current I is uniformly distributed across this cross-section. The magnetic field is (1) inversely proportional to r in the region r < a and uniform throughout in the region r > a (2) directly proportional to r in the region r < a and inversely proportional to r in the region r > a (3) zero in the region r < a and inversely proportional to r in the region r > a (4) uniform in the region r < a and inversely proportional to distance r from the axis, in the region r > a
- (1) inversely proportional to r in the region r < a and uniform throughout in the region r > a
- (2) directly proportional to r in the region r < a and inversely proportional to r in the region r > a
- (3) zero in the region r < a and inversely proportional to r in the region r > a
- (4) uniform in the region r < a and inversely proportional to distance r from the axis, in the region r > a
Correct answer: (2) directly proportional to r in the region r < a and inversely proportional to r in the region r > a
Solution
The magnetic field inside a uniformly current-carrying wire increases linearly with distance from the center due to the contribution of the current within the radius, while outside the wire, the field decreases inversely with distance from the wire, following Ampère's law.
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