Question

Learning Goal:

The goal of the problems is to determine the net magnetic field in regions around two current carrying wires. There are 4 independent sets of problems: (i) parts A and B form one set problems; (ii) parts C and D form a second set problems; (iii) part E comprises the third set; and (iv) part F forms the last set.

Use the following coordinate system for the following problems:

(i) the positive z direction (+z) is straight up

(ii) the negative z direction (-z) is straight down

(iii) the positive x direction (+x) points perpendicularly out of the plane of the screen

(iv) the negative x direction (-x) points perpendicularly into of the plane of the screen

(v) the positive y direction (+y) points to the right

(vi) the negative y direction (-y) points to the left

Part A

A transmission wire oriented parallel to the x-axis carries a current of   200 A   flowing along the +x direction. A second transmission wire also oriented parallel to the x-axis but lying at a perpendicular distance of   1.20 m   below the first wire carries a current of   240 A flowing along the +x direction.

What is the magnitude of the total magnetic field at a point midway between the two wires?

Express your answer to three significant figures and include the appropriate units.

(Hint: The magnitude of the magnetic field at P due to each current is easy to compute. Use the right hand rule to determine the direction of the direction of the magnetic fields and sum them.)

Part B

What is the direction of the net magnetic field in part A?

A) -x

B) +x

C) -z

D) +z

E) +y

F) -y

I will rate answers. Thank you.

Answer 1

Both the wires carry a current flowing in the same direction (positive x direction).

Using Ampere's law, the magnitude of total magnetic field at the midpoint of the two wires will be:

$B_{tot} =\frac{\mu_oI_1}{2\pi (d/2)}+ \frac{\mu_oI_2}{2\pi (d/2)} = \frac{\mu_o}{2\pi}\left(\frac{240}{1.2/2} - \frac{200}{1.2/2} \right ) = 13.33\mu T$

Since the lower wire carries a larger current, the magnetic field due to it will be larger than the magnetic field due to the upper wire. So, from Right-hand thumb rule, the direction of this net magnetic field will be outwards (out of the plane of paper). This is the +x direction [answer - B]