devarshi-dt-logo

Question:

A magnetic compass needle oscillates 30 times per minute at a place where the dip is 45o, and 40 times per minute where the dip is 30o. If B1 and B2 are respectively the total magnetic field due to the earth at the two places, then the ratio B1/B2 is best given by:

2.2

1.8

0.7

3.6

Solution:

Correct option is C. 0.7
f1=1/2π√μB1cos 45o
f2=1/2π√μB2cos 30o
f1/f2=√(B1cos 45o)/(B2cos 30o)
∴B1/B2 = (f1/f2)² * (cos 30o/ cos 45o) = (30/40)² * (√3/2)/(1/√2) = (9/16) * √3 = 0.7