GATE-2018 (24) :Wyllie – Time average equation

94. The transmitter of a time domain EM system is in the form of a circular loop. If the radius of the loop is doubled and the current is reduced by half, the dipole moment of the system will

A) decrease to half its original value
B) decrease to one-fourth its original value
C) increase by a factor of two
D) increase by a factor of four

Answer: C

Explanation:

Formula:

Dipole moment = product of transmitter current and area

Area of the circle (A)= 4*pi* r^2 ----------------(1)

r- radius of the circle


The dipole moment in normal case= I * 4*pi* r^2

                                                        = 4*pi* I*r^2 ------------(2)

I- current

The dipole moment in above case,

 If the radius of the loop is doubled and the current is reduced by half,

r = 2r

I= I/2

substitute in equation (1) 

 Area = 4* pi* (2r)^2

          = 16*pi* r^2 

current I= I/2

substitute  area and current values  in equation  (2)

Dipole moment = 16*pi*r^2 *(I/2)

                        = 8* pi * I * r^2 ------------(3)

Therefore form equation (1) and (2) dipole moment increases factor of two.





for more details follow this link:

https://archive.epa.gov/esd/archive-geophysics/web/html/time-domain_electromagnetic_methods.html