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Two identical coils having same number of turns and carrying equal current have common centre and their planes are at right angles to each other. What is the ratio of magnitude of the resultant magnetic field at the centre and the magnetic field due to one of the coils at the centre ?

Asked in GUJCET 2007 · Rotating charges and multiple loops

• (1) √2 : 1
• (2) 1 : √2
• (3) 2 : 1
• (4) 1 : 1

Step-by-step solution

Why the other options are wrong

• (2) The reciprocal of the ratio asked for. The resultant is the larger of the two fields, so resultant : single must exceed 1.
• (3) Comes from adding the two fields as plain numbers, B+B=2B. Their directions are at right angles, so they combine as √B²+B², not as a sum.
• (4) Assumes a field at right angles cannot change the magnitude. Two equal perpendicular vectors give a resultant √2 times either one.

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