Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 12

# The Combination of Two Bar Magnets Makes 10 Oscillations per Second in an Oscillation Magnetometer When like Poles Are Tied Together and 2 Oscillations per Second When Unlike Poles Are Tied Together. - Physics

Sum

The combination of two bar magnets makes 10 oscillations per second in an oscillation magnetometer when like poles are tied together and 2 oscillations per second when unlike poles are tied together. Find the ratio of the magnetic moments of the magnets. Neglect any induced magnetism.

#### Solution

Given :
Number of oscillations per second made by the combination of bar magnets with like poles, V_1 = 10 s^-1

Number of oscillations per second made by the combination of bar magnets with unlike poles, V_2 = 2  s^-1

The frequency of oscillations in the magnetometer (V) is given by

V = 1/(2pi) sqrt((MB_H)/I)

When like poles are tied together, the effective magnetic moment is M = M_1 - M_2

When unlike poles are tied together, the effective magnetic moment is M = M_1 + M_2

As the frequency of oscillations is directly proportional to the magnetic moment ,

V_1/V_2 = sqrt((M_1 - M_2)/(M_1 + M_2))

⇒ (10/2)^2 = (M_1 - M_2)/(M_1 + M_2)

⇒ 25/1 = (M_1 - M_2)/(M_1 + M_2)

⇒ (25 + 1)/(25 - 1) = (M_1 - M_2+M_1 + M_2)/(M_1 - M_2-M_1-M_2)

⇒ 26/24 = (2M_1)/(-2M_2)

⇒ M_1/M_2 = -26/24 = -13/12

Hence, the ratio of the effective magnetic moment is -13/12

Is there an error in this question or solution?

#### APPEARS IN

HC Verma Class 11, Class 12 Concepts of Physics Vol. 2
Chapter 14 Permanent Magnets
Q 22 | Page 278