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

Open in App

Solution

We know v = $\frac{1}{2 π} \sqrt{\frac{m B_{H}}{1}}$

For like poles tied together

M= $M_{1} - M_{2}$

For unlike pole

M' = $M_{1} + M_{2}$

$\frac{v_{1}}{v_{2}} = \sqrt{\frac{M_{1} - M_{2}}{M_{1} + M_{2}}}$

$\Rightarrow {(\frac{10}{2})}^{2} = \frac{M_{1} - M_{2}}{M_{1} + M_{2}}$

$\Rightarrow \frac{25}{1} = \frac{M_{1} - M_{2}}{M_{1} + M_{2}}$

$\Rightarrow \frac{25 + 1}{25 - 1} = \frac{M_{1} - M_{2} + M_{1} + M_{2}}{M_{1} - M_{2} - M_{1} - M_{2}}$

$\Rightarrow \frac{26}{24} = \frac{2 M_{1}}{- 2 M_{2}}$

$\Rightarrow \frac{M_{1}}{M_{2}} = - \frac{26}{24} = - \frac{13}{12}$

Suggest Corrections

Similar questions

Q. A combination of two bar magnets, in vibration magnetometer, makes

10

oscillations per second if their like poles are tied together and

2

oscillations per second when unlike poles are tied together. If induced magnetism is neglected, then the ratio of their magnetic moments is

Q. Two magnets are held together in a variation magnetometer and are allowed to oscillate in the earth's magnetic field with like poles together. 12 oscillations per minute are made but for unlike poles together only 4 oscillations per minute are executed. The ratio of their magnetic moments is

Q. A combination of two magnets perform

10

oscillations per minute with similar poles together and

6

oscillation per min with dissimilar poles together. The ratio of magnetic moments is.

Two bar magnets are placed in a Vibration Magnetometer and allowed to vibrate. They make $20$ oscillations per minute when their similar poles are on the same side and they make $15$ oscillations per minute with their opposite poles lie on the same side. The ratio of their moments is :

Q. Two magnets are placed one above the other with like poles together the time period of this combination is

10

seconds. Now they are placed one above the other with unlike poles together the time period of this combination is

20

second in the same field.The ratio of magnetic moments is

Join BYJU'S Learning Program

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

We know v = 12π√mBH1 For like poles tied together M= M1−M2 For unlike pole M' = M1+M2 v1v2=√M1−M2M1+M2 ⇒(102)2=M1−M2M1+M2 ⇒251=M1−M2M1+M2 ⇒25+125−1=M1−M2+M1+M2M1−M2−M1−M2 ⇒2624=2M1−2M2 ⇒M1M2=−2624=−1312