Question

At a certain location in the Philippines, Earth’s magnetic field of $\mathbf{39}\mathbf{\mu T}$is horizontal and directed due north. Suppose the net field is zero exactly$\mathbf{8}\mathbf{.}\mathbf{0}\mathbf{}\mathbf{cm}$above a long, straight, horizontal wire that carries a constant current. (a) What are the magnitude and (b) What is the direction of the current?

Short answer

a. The magnitude of the current is$16\text{A}$ .

b. The direction of the current is east.

Step-by-step solution

Determining the formula for the magnetic field 

Biot- savart law states that the magnetic intensity at any point due to a steady current in an infinitely long straight wire is directly proportional to the current and inversely proportional to the distance from the point to the wire. Using this equation, Solve for current.

Magnetic field due to the current in the wire at a point and distance r from the wire is:

$\mathbf{B}\mathbf{=}\frac{{\mathbf{\mu }}_{\mathbf{0}}\mathbf{i}}{\mathbf{2}\mathbf{\pi r}}$

(a) Calculating magnitude of the current  

To find the magnitude of current :

$B=\frac{{\mu }_{0}i}{2\pi r}$

Substitute the value and solve as:

$$\begin{gathered} i=\frac{2\pi rB}{{\mu }_0} \\ =\frac{2\pi \times 0.08\times 39\times {10}^{-6}}{4\pi \times {10}^{-7}} \\ =16\text{A} \end{gathered}$$

(b) Calculating the direction of the current 

Direction of the current:

As the field is directed towards south, the current must be directed from west to east as per the right hand rule.