A wire placed along north south …
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Gaurav Seth 4 years, 10 months ago
Using Biot-Savart's law:
%5C%5C%5C%5Cl%3D100%5Csqrt2-d%5C%20cot%5Ctheta%2C%5C%20%5C%20dl%3Dd%5C%20cosec%5E2%5Ctheta%20d%5Ctheta%5C%5Cr%3Dd%5C%20cosec%5Ctheta%5C%5C%5C%5CdB%3D%5Cfrac%7B%5Cmu_0%20i%7D%7B4%20%5Cpi%20d%7Dsin%5Ctheta%20d%5Ctheta%2C%5C%20%5C%20%5C%20----(2)%5C%5C%5C%5CB%3D%5Cfrac%7B%5Cmu_0%20i%7D%7B4%20%5Cpi%20d%7D(Cos%5Ctheta_1%20-%20Cos%5Ctheta_2)%5C%20%5C%20%5C%20%5C%20----(3)%5C%5C%5C%5Cd%5Ctheta%3D%5Cfrac%7Bdl%5C%20sin%5Ctheta2%7D%7Br%7D%3D%5Cfrac%7B1cm*sin%5C%2045%5E0%7D%7B200cm%7D)
Here, the length of wire segment is so small compared to the distance of the point, we can use any of the 3 formulas above to find dB or B.
Using (3) is difficult as finding θ1 and θ2 and their Cosine is tough. So use either (1) or (2) directly.
Using (1):
dB = 10⁻⁷ units * 5A * 0.01 m * Sin 45⁰ / (2 m) ² Tesla
= 1.77 * 10⁻⁷ Tesla
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1Thank You