Which one of the following graphs accurately represents the variation of magnetic field (B) with distance (r) from the exact center of a solid, current-carrying cylindrical wire of radius R?
A. B is zero everywhere inside, and inversely proportional to r outside.
B. B is constant inside, and directly proportional to r outside.
C. B is inversely proportional to r everywhere.
D. B is directly proportional to r inside, and inversely proportional to r outside.
Answer: Option D
Solution (By JKSSB Mock Tests)
By Ampere's Circuital Law, for a solid wire carrying uniform current, the magnetic field inside (r < R) is B = (mu_0 * I * r) / (2piR^2), meaning B ∝ r (straight line). Outside the wire (r > R), B = (mu_0 * I) / (2pi*r), meaning B ∝ 1/r (rectangular hyperbola). Thus, it increases linearly then decays.
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