G straight wires are parallel and a distance 5 m apart. If both wires carry a current of 2 A in the same direction, what is the magnetic field between the wires at a distance of 3.3 m as measured below the top wire? Note sign denotes direction

Explanation:

Given that,

Current in each wire is 2A

Therefore, i1 = i2 = 2A

The wire are 5m apart

We want to find a magnetic field at a distance 3.3m

Magnetic Field on wire is given as

B= μoI/2πr

Where,

μo is a constant = 4π×10^-7 Tm/A

r is the distance between the two wires

I is the current in the wires

B is the magnetic field

Then, the magnetic field at point 3.3m can be determined by finding the resultant of both magnetic field at that point, .

B = B1 + (-B2)

B = B1 — B2.

If the distance of first wire from the point where will want to find the magnetic field is 3.3m

r1 = 3.3m

Then, the distance of B2 from the same point will be

r2 = 5-3.3 = 1.7m, since the total distance from the wires is 5m.

Then,

B = B1—B2

B = μoI1/2πr1 — μoI2/2πr2

I1 = I2 = I

B = μoI/2πr1 — μoI/2πr2

B = 4π × 10^-7 × 2/2π ×3.3 — 4π×10^-7×2/2π×1.7

B =1.21×10^-7 — 2.35×10^-7

B = — 1.14×10^-7 T

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