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

The current in second wire is 5.0 A.

(B) is correct option.

Step-by-step 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=(\mu_(0)I)/(2\pi r)`

Where, I = current

r = distance

Put the value into the formula

For first wire

`B = (\mu_(0)*3.7)/(2\pi *3.4*10^(-2))`...(I)

For second wire,

The distance is 8-3.7 = 4.3 cm

`B' = (\mu_(0)* I')/(2\pi *(8-3.4)*10^(-2))`...(II)

The magnetic field in both the wires,

From equation (I) and (II)

`(\mu_(0)*3.7)/(2\pi *3.4*10^(-2))= (\mu_(0)* I')/(2\pi *(8-3.4)*10^(-2))`

`I'=(3.7*4.3*10^(-2))/(3.4*10^(-2))`

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

Hence, The current in second wire is 5.0 A.