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# A cell is connected across two points P and Q of uniform circular conductor . prove that the magnetic field at it Centre is 0

aritra maity
42 Points
4 years ago
As conductor is connected with the cell , the potential difference across two paths (two possible paths i.e. one upside and one downside path) is same.
V= V2
I1R1=I2R2
I1dl1=I2dl(as resistivity and area of cross section same )

Now,
field, due to one path, is opposite due to another part. So magnetic field at the center is
$\frac{\mu }{4\pi }i1dl1\sin \Theta - \frac{\mu }{4\pi }i2dl2\sin \Theta$
[sin 90 = 1 , i1dli2dl2]
= 0 (proved)