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What is tangent law ? Discuss in detail. |
Answer» Solution :Tangent LAW :  (i) A MAGNETIC needle suspended, at a point where there are two crossed magnetic frelds acting at RIGHT angles to each other, will come to rest in the direction of the resultant of the two fields. (ii) `B_(1) " and " B_(2)` are two uniform magnetic fields acting at right angles to each other. (iii) A magnetic needle placed in these two fields will be subjected to two torques tending to ritatethe MAGNET in opposite directions. (iv) The torque `tau_(1)` due to the two equal and opposite parallel forces `mB_(1)" and " mB_(1)` tend to set the magnet parallel to B 1. Similarly the torque `tau_(2)` due to the two equal and opposite parallel forces `mB_(2)" and " mB_(2)`tends to set the magnet parallel to`B_(2)`. In a position where the torques balance each other, the magnet comes to rest. Now the magnet makes an angle `theta ` with `B_(2)`as shown in the Fig. The deflecting torque due to the forces, `mB_(1)" and " mB_(1)` `tau_(1) = mB_(1) xx NA` ` = mB_(1) xx NS cos theta ` ` = mB_(1) xx 2l cos theta ` ` = 2l mB_(1) cos theta ` ` :. "" tau_(1) = MB_(1) cos theta` Similarly the restoring torque due to the forces `mB_(2)" and "mB_(2)` `tau_(2) = mB_(2) xx SA` ` = mB_(2) xx 2l SIN theta ` ` = 2lm xx B_(2) sin theta` ` tau_(2) = MB_(2) sin theta ` At equillibrium , `tau_(1) = tau_(2)` ` :. "" MB_(1) cos theta= MB_(2) sin theta ` ` :. "" B_(1) = B_(2) tan theta ` This is called Tangent law Invariably , in the applications of tangent law,the restoring magnetic field `B_(2)` is the horizontal component of Earth's magnetic field `B_(h) `. |
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