Question

A wire carries 3.7 A of current. A second wire is placed parallel to the first 8.0 cm away. What is the current flowing through the second wire if the magnitude of the wires is zero at a distance 3.4 cm from the first wire. O 11 A 5.0A O 5.7A O 3.7A

Answer 1

Answer:

The current in second wire is 5.0 A.

(B) is correct option.

Explanation:

Given that,

Current in first wire = 3.7 A

Distance = 8.0 cm

We need to calculate the magnetic field due to the current carrying wire

Using formula of magnetic field

$B=\dfrac{\mu_{0}I}{2\pi r}$

Where, I = current

r = distance

Put the value into the formula

For first wire

$B = \dfrac{\mu_{0}\times3.7}{2\pi \times3.4\times10^{-2}}$...(I)

For second wire,

The distance is 8-3.7 =  4.3 cm

$B' = \dfrac{\mu_{0}\times I'}{2\pi \times(8-3.4)\times10^{-2}}$...(II)

The magnetic field in both the wires,

From equation (I) and (II)

$\dfrac{\mu_{0}\times3.7}{2\pi \times3.4\times10^{-2}}= \dfrac{\mu_{0}\times I'}{2\pi \times(8-3.4)\times10^{-2}}$

$I'=\dfrac{3.7\times4.3\times10^{-2}}{3.4\times10^{-2}}$

$I'=4.68\ A\ approx = 5.0\ A$

Hence, The current in second wire is 5.0 A.