Question

A wire placed along the north-south direction carries a current of  8 A  from south to north. Find the magnetic field due to a  1 cm  piece of wire at a point  200 cm  north-east from the piece??​

Answer 1

From question we have,

• Current passing through it is 8 A
• Distance if point from the wire
• And it is in north east direction

Now, as it is in north east direction, surely it will form 45° angle, let point whose magnetic field we need to find be p.

• Now, according to the diagram in the attachment, angle at P is 45° and the angle near it is 45° so,

We know that,

• B = μ0i/4πr ( Sinθ1 + Sinθ2 )
• B = μ0 × 8 /4π(200) ( 45 + 45 )
• B = μ0 × 8 /800π ( 1/√2 + 1/√2 )
• B = μ0 /100π × √2
• B = 4π × 10⁻⁷ × √2/100 π
• B = 4√2 × 10⁻⁷ × 10-²
• B = 4√2 × 10⁻⁹ T

Therefore, the magnetic field will be 4√2 × 10⁻⁹ T.

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I really apologize, if I'm wrong about the answer. Although, I've tried my best to make it error free.