Two circular coils made of same material having radii `20 cm & 30 cm` have turns `100 & 50` respectively. If they are connected `a )` in series `b)` in parallel `c)` separately across a source of same emf find the ratio of magnetic inductions at the centre of circles in each case

Explanation

a) `B = (mu_0 "ni")/(2r) ` , coils are in series `rArr` I is same in both `B prop n/r , B_1/B_2 = 100/50 xx 30/20 = 3:1`
b) coils are parallel `rArr` potential difference is ame `iprop1/R` where `R = (rho (npir))/(A) ` , where A is area of cross section of wire which is ame for both
`rArr R prop nr , iprop (1)/(nr) " bur " B_0 = (mu_0 "ni")/(2r) rArr B prop n/r xx (1)/(nr) rArr B prop (1)/(r^2)`
` therefore B_1/B_2 = (30/20)^2 = 9/4`
c) for the coils ,potential difference is same
`iprop 1/R " where " R = (rho (npir))/(A), R prop nr `
` I prop (1)/(nr) rArr B_0 prop (1)/(r^2) , therefore B_1/B_2 = 9/4`