Two circular copper coils of radii 10 cm and 20 cm and having the same number of turns, are connected in parallel. The two copper wires have the same area of cross-section. What is the ratio of the magnetic inductions at the centres of the coils ?

Options

A. `2:1`
B. `3:1`
C. `4:1`
D. `5:1`

Answer

C

Explanation

The coils are connected in parallel.
`thereforeI_(1) =(V)/(R_(1))and I _(2)=(V)/(R_(2))`
` therefore (I _(1))/(I_(2)) =(R_(2))/(R_(1))But R =(rhoL)/(A)`
As `rho` and A are the same for both the wires
`(R_(2))/(R_(1))=(L_(2))/(L_(1))=(2pi r_(2)n)/(2opi r _(1)n)=(r_(2))/(r _(1))=(20)/(10) =2/1`
`therefore (I_(1))/(I_(2))=(R_(2))/(R_(1))=(r_(2))/(r _(1))=2/1`
But the field at the centre of a coil is `B = (mu_(0))/(4pi) ((2pi nI)/(r))`
`therefore B propI/r`
or `(B_(1))/(B_(2))=(I_(1))/(r_(1))xx(r_(2))/(I_(2))=((I_(1))/(I_(2)))((r_(2))/(r_(1))`
`=2/1 xx2/1 =4/1`