Question

Two similar conductors carrying same amount of current are placed as shown in the figure given below. The plane on one conductor is along x-axis and other is along y-axis. What is the ratio of resultant magnetic field at a common point to the individual magnetic field?​

Answer 1

Answer:

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Answer 2

Given: Two similar conductors carrying the same amount of current are placed such that one conductor is along the x-axis and the other is along the y-axis

To find: the ratio of the resultant magnetic field at a common point to the individual magnetic field

Solution: Since both, the conductor is identical and carries the same amount of current

So we can let the Magnetic field of both the conductor be B1 and B2

we can write it as

B1 = B2 = B

Net magnetic field at the common point of the conductors will be

Bnet = √( B1^2 + B2^2)

Bnet = √( B^2 + B^2)

Bnet = √2 B

The required ratio will be Bnet/B

Bnet/B = √2 B/B

Bnet/B = √2/1

therefore, the ratio of resultant magnetic field at a common point to the individual magnetic field will be √2:1.