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  • (a) State Biot – Savart law and express this law in the vector form. (b) Two identical circular coils, P and Q each of radius R, carrying currents 1 A and <img alt="\sqrt{3}A" src="https://entrancecorner.codecogs.com/gif.latex?%5Csqrt

(a) State Biot – Savart law and express this law in the vector form.
(b) Two identical circular coils, P and Q each of radius R, carrying currents 1 A and \sqrt{3}A respectively, are placed concentrically and perpendicular to each other lying in the XY and YZ planes. Find the magnitude and direction of the net magnetic field at the centre of the coils.

 

 

Answers (1)

a) According to Biot - Savart's law the magnetic field due to a current  element at a distance r from the element is

directly proportional to

(1) Current I

(2) length of the element dl

(3) The sine of the angle between the line joining the current element and the point and inversely proportional to the square of the distance between the point and the current element.

dB\alpha \frac{Idl\; \sin \theta }{r^{2}}

dB= \frac{\mu_{o} }{4\pi}\; \frac{Idl\; \sin \theta }{r^{2}}

In Vector form

\overrightarrow{dB}= \frac{\mu_{o} }{4\pi}\; \frac{Idl\times \vec{r} }{r^{3}}

(b) Magnetic field due to P is

B_{1}=\frac{\mu_{o}I}{2R}\widehat{k}

Magnetic field due to Q

B_{2}=\frac{\mu_{o}\sqrt{3}I}{2R}\widehat{i}

Net magnetic field magnitude is

B= \sqrt{B{_{1}}^{2}+B{_{2}}^{2}}=\frac{\mu_{o}I}{R}

Direction is \tan ^{-1}(\sqrt{3})=60^{o} with  B_{1}

Posted by

Safeer PP

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