Physics-
General
Easy

Question

What will be the resultant magnetic field at origin due to four infinite length wires. If each wire produces magnetic field 'B' at origin

  1. 4 B    
  2. square root of 2 B    
  3. 2 square root of 2 B    
  4. Zero    

The correct answer is: 2 square root of 2 B


    Direction of magnetic field (B1, B2, B3 and B(d) at origin due to wires 1, 2, 3 and 4 are shown in the following figure.
    B subscript 1 end subscript equals B subscript 2 end subscript equals B subscript 3 end subscript equals B subscript 4 end subscript equals fraction numerator mu subscript 0 end subscript over denominator 4 pi end fraction. fraction numerator 2 i over denominator x end fraction equals B. So net magnetic field at origin O
    B subscript n e t end subscript equals square root of left parenthesis B subscript 1 end subscript plus B subscript 3 end subscript right parenthesis to the power of 2 end exponent plus left parenthesis B subscript 2 end subscript plus B subscript 4 end subscript right parenthesis to the power of 2 end exponent end root equals square root of left parenthesis 2 B right parenthesis to the power of 2 end exponent plus left parenthesis 2 B right parenthesis to the power of 2 end exponent end root equals 2 square root of 2 B

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