Question 7.13: A square loop of sides 2d is placed with its sides parallel ...
A square loop of sides 2d is placed with its sides parallel to an infinitely long conductor carrying current I. The centre line of the square is at a distance b form the conductor. Determine the expression for the total flux passing through the loop. What would be the loop flux if the loop is placed such that the conductor is normal to the plane of the loop? Does the loop flux in this case depend upon its relative location wrt the conductor?
With reference to Fig. 7.31, at a distance r from the conductor.
H= I/(2π r) A/m (Ampere’s law)
B = µ_{0} H = µ_{0} I/(2 π r) T
The flux passing through elemental strip (width dr)
d \phi = B dA = (µ_{0}I/2 π r) × (2d) dr
Integrating, we get
\phi = (µ_{0} I d/π) \int_{b – d}^{b + d} \frac{dr}{r} = \frac{µ_{0} I d}{π} ln \left\{\frac{b + d}{b – d} \right\}
If the conductor is normal to the plane of the loop, (regardless of its relative location) the flux through the loop is zero.
