Question

SP 15The magnetic field in a region of space is measured to be:This field is known to be caused by a cluster of long-straight wires that are parallel to the z-axis. Find how much and in which direction the net current is flowing through the wires that pass through the rectangle whose corners are positioned at these points in the x, y plane: (0 cm, 0 cm), (2 cm, 3 cm), (3 cm, 0 cm)

Answer 1

i = 0.477 10⁴ B

the current flows in the counterclockwise

Step-by-step explanation:

For this exercise let's use the Ampere law

∫ B . ds = μ₀ I

Where the path is closed

Let's start by locating the current vines that are parallel to the z-axis, so it must be exterminated along the x-axis and as the specific direction is not indicated, suppose it extends along the y-axis.

From BiotSavart's law, the field must be perpendicular to the direction of the current, so the magnetic field must go in the x direction.

We apply the law of Ampere the segment parallel to the x-axis is the one that contributes to the integral, since the other two have an angle of 90º with the magnetic field

Segment on the y axis

L₀ = (y2-y1)

L₀ = 3-0 = 3 cm

Segment on the point x = 2 cm

L₁ = 3-0

L₁ = 3cm

B L = μ₀ I

B 2L = μ₀ I

i = 2 L B /μ₀

i= 2 0.03 / 4π 10⁻⁷ B

i = 4.77 10⁴ B

The current is perpendicular to the magnetic field whereby the current flows in the counterclockwise