You are looking straight down on a magnetic compass that is lying flat on a tabl

Question

You are looking straight down on a magnetic compass that is lying flat on a table. A wire is stretched horizontally under the table, parallel to and a short distance below the compass needle. The wire is then connected to a battery so that a current I flows through the wire. This current causes the north pole of the compass needle to deflect to the left. The questions that follow ask you to compare the effects of different actions on this initial deflection. If the wire is lowered farther from the compass, how does the new angle of deflection of the north pole of the compass needle compare to its initial deflection? You did not open hints for this part. It is larger. It is smaller. It is unchanged.

Explanation / Answer

As torque on the needle placed in the magnetic field of wire (B) with current I is

=MB                                                    where M=magnetic moment of needle.

Also as magnetic field due to current carrying wire (B) depends on 1/r^2

So, B will decrease as wire is lowered from table as r increase.

So torque () will decrease,

Hence angle of deflection on the needle will decrease as wire is lowered.

So, correct option is (B) it is smaller.

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