Two magnets are kept one above the other and made to oscillate in horizontal plane. The period combination is 6 second. When one of the magnets is reversed pole to pole, the period of oscillations of combination is 3 second. Compare the magnetic pole moments of the two magnets.

Open in App

Solution

Given,

Two magnets,

$T_{A} = 6 s, T_{B} = 3 s$

So,

$M_{A} = N e t = M_{1} + M_{2}$

Similarly,

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

$T_{A} = 6 s$

$T_{A} = 2 π \sqrt{\frac{I}{M_{A} B}}$

$T_{B} = 4 π \sqrt{\frac{I}{M_{B} B}}$

Therefore,

$(\frac{T_{A}}{T_{B}})^{2} = \frac{M_{B}}{M_{A}} = \frac{M_{1} - M_{2}}{M_{1} + M_{2}}$

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

$4 M_{1} + M_{2} = M_{1} - M_{2}$

$4 M_{1} + 4 M_{2} = M_{1} - M_{2}$

$3 M_{1} = 5 M_{2}$

$\frac{M_{1}}{M_{2}} = \frac{5}{3}$

Thus, the magnetic pole moments of the two magnets is:

$\frac{M_{1}}{M_{2}} = \frac{5}{3}$

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. 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.

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

Q. Two bar magnets of same length and breadth having magnetic moments

M

and

4 M

respectively are joined with likes poles together and suspended in a uniform magnetic field

B

, it oscillates with time period

T = \sqrt{3} s

. If the polarity of one of the magnet is reversed and the combination is again made to oscillate in the same field. Find the new time period of this combination.

If two identical bar magnets, each of length $l$ , pole strength $m$ and magnetic moment $M$ are placed perpendicular to each other with their unlike poles in contact, the magnetic moment of the combination is

Join BYJU'S Learning Program

Two magnets are kept one above the other and made to oscillate in horizontal plane. The period combination is 6 second. When one of the magnets is reversed pole to pole, the period of oscillations of combination is 3 second. Compare the magnetic pole moments of the two magnets.

Given,Two magnets,TA=6s,TB=3sSo,MA=Net=M1+M2Similarly,MB=M1−M2TA=6sTA=2π√IMABTB=4π√IMBBTherefore,(TATB)2=MBMA=M1−M2M1+M2⇒4=M1−M2M1+M24M1+M2=M1−M24M1+4M2=M1−M23M1=5M2M1M2=53Thus, the magnetic pole moments of the two magnets is:M1M2=53