Answer 1

Given :
Horizontal component of Earth's magnetic field,`B_H = 3.6 xx 10^-5  "T"`

Deflection shown by the tangent galvanometer, `θ = 45^circ`

Current through the galvanometer, `l = 10  "mA" = 10^-2  "A"`

Radius of the coil, r = `10  "cm" = 0.1  "m"`

Number of turns in the coil, n = ?

We know , 

`B_H tan θ = (u_0 In)/(2r)`

⇒ `n = (B_H tan  \ θ  xx 2r)/(u_0I)`

⇒ `n = (3.6 xx 10^-5 xx 2 xx 1 xx 10^-1)/(4pi xx 10^-7 xx 10^-2)`

⇒ `n = 0.57332 xx 10^3 = 573`