A loop ABCDA, carrying current 
, is placed in a plane, consists of two semi-circular segments of radius 
and 
. The magnitude of the resultant magnetic field at center O is 
. The value of k is .
(Given 
Text Solution
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(1)
Magnetic Field from Semi-Circular Segments:
The magnetic field at the center due to a semicircular loop is given by:
Calculating 
and 
:
For the semi-circle with radius 
:
For the semi-circle with radius 
:
Net Magnetic Field at the Center (0):
The total magnetic field 
at the center is the difference between these two fields (since they are in opposite directions):
Calculate:
Value of 
:
Given that the magnitude of the resultant magnetic field is 
, we find 
.
Thus, the value of 
is 1.
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