1.

A magnetic needle of length 10 cm, suspended at its middle point through a thread, stays at an angle of 45^(@) with the horizontal. The horizontal component of the earth's magnetic lield is 18 muT, Which of the following statement(s) is//are correct.

Answer»

VERTICAL component of magnetie field, `B_(V) = 18 muT`.
Without the applied force the needle will stay m the direction of the resultant magnetic field of the EARTH.
When the force is applied the needle will stay in horizontal position.
A vertical Torce of `F =5.8 xx 10^( -5) N`, should be applied we end so as to keep it in horizontal position when the pole strength of the needle is 1.6Am.

Solution :Without the applied force, the needle will stay in the direction of the resultant magnetic field of the Earth. Thus the dip `delta` at the place is `45^(@)`From figure (i),
`tan45^(@) = B_(v)//B_(H) = 18muT`
When the force F is applied figure (II), the needle stays in horizontal position Taking torque about the centre of the magnet,
`2mB_(V) xx L = F xx l`
or `F =2mB_(V)`
`=2 xx (1.6 Am ) xx (18 xx 10^(-6)T) = 5.8 xx 10^(-5)N`


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