Question:
A thick current carrying cable of radius $'R'$ carries current $'I'$ uniformly distributed across its cross-section. The variation of magnetic field $B ( r )$ due to the cable with the distance $'r'$ from the axis of the cable is represented by :
A thick current carrying cable of radius $'R'$ carries current $'I'$ uniformly distributed across its cross-section. The variation of magnetic field $B ( r )$ due to the cable with the distance $'r'$ from the axis of the cable is represented by :
Updated On: Jul 1, 2024
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The Correct Option is C
Solution and Explanation
$B \propto r(0 \leq r \leq R)$
$B \propto \frac{1}{r}(r \geq R)$
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Concepts Used:
Amperes circuital law
According to Ampere’s law, magnetic fields are related to the electric current that is produced in them. This law specifies that the magnetic field is associated with a given current or vice-versa, provided that the electric field doesn’t change with time.
Ampere’s circuital law can be written as the line integral of the magnetic field surrounding the closed loop which is equal to the number of times the algebraic sum of currents passing through the loop.
According to the second equation, if the magnetic field is integrated along the blue path, then it is equal to the current enclosed, I.
The magnetic field doesn’t vary at a distance r because of symmetry. The path length (in blue) in figure 1 has to be equal to the circumference of a circle,2πr.
