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Unformatted text preview: 49 The integral I = & & L x ) x ( B x d x d can be evaluated to give, [ ] 2 2 2 m d L d d B I- + =------------------------------- (15) I.5. Determination of B m : The value of B m is determined from the period of oscillation of the magnetometer needle. The magnetometer is placed at the center in place of CRT so that the magnets are at a distance of d from it (see fig4). The magnetometer needle aligns itself along the resultant magnetic field fig 4 2 m 2 E B B B + = where B E is the earths magnetic field acting towards south . A small disturbance of the needle about the equilibrium position causes it to oscillate. The angular frequency of small oscillations can be easily shown to be (Exercise 7) I B = , where & is the magnetic moment of the needle and I its moment of inertia, and hence the time period of small oscillations B I 2 T = . Now, the resultant magnetic field m 2 m 2 E sin / B B B B = + = . Thus 2 2 m T Sin I 4 B = In the absence of the magnets B=B...
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- Fall '09