The correct option is A is true but R is false
Explanation
The magnitude of the magnetic field produced by a current-carrying conductor is determined by the strength of the current and the distance from the conductor. For a long straight wire, this relationship is derived from the Biot-Savart Law or Ampere’s Circuital Law.
Statement-wise Analysis:
- Assertion (A): Correct
The magnetic field ($B$) at a distance ($r$) from a straight wire carrying current ($I$) is given by the formula:
$B = \frac{\mu_{0}I}{2\pi r}$
This equation indicates that the magnetic field is inversely proportional to the distance from the wire ($B \propto \frac{1}{r}$). Consequently, as the distance from the wire increases, the strength of the magnetic field decreases. - Reason (R): Incorrect
The reason claims that magnetic field strength is directly proportional to the distance ($B \propto r$). This is factually incorrect. As established by the formula above, the relationship is inversely proportional. Direct proportionality would imply that the magnetic field strengthens as one moves further away from the source, which violates physical principles.
Key Takeaway:
The magnetic field strength due to a straight current-carrying wire is directly proportional to the current flowing through it ($B \propto I$) and inversely proportional to the perpendicular distance from the wire ($B \propto \frac{1}{r}$).