Question

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.

Answer 1

The ratio of the magnetic moments of the magnets is -13/12

Explanation:

Step 1:

Number of oscillations per second, by combining bar magnets with adjacent poles ,$V_1= 10 s^{-1}$

Amount of oscillations per second produced by integrating bar magnets with poles unlike, $V_2 = 2 s^{-1}$

The oscillation frequency of the magnetometer is determined by

$v=\frac{1}{2 \pi} \sqrt{\frac{M B_{H}}{I}}$

Step 2:

The efficient magnetic moment when bound like poles is $M = M_1 -M_2$

If unlike poles, the efficient magnetic moment is bound together$M = M_1 + M_2$

As oscillation frequency is directly proportional to the magnetic moment

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

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

  $\frac{100}{4}=\frac{M_{1}-M_{2}}{M_{1}+M_{2}}$

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

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

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

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

So the effective magnetic moment ratio is -13/12.

Answer 2

Explanation:

answer is= -13/12

correct solutions