Two parallel straight wires 10 cm apart, carry currents in opposite directions. The first
wire carrying current is out of the page, and the second one carrying current
is into the page. The magnitude of the magnetic field halfway between the two
wires is:
(A)
(B)
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(D) Zero

To find the magnetic field halfway between two parallel wires carrying currents in opposite directions, we can use the formula for the magnetic field around a long straight conductor:

Where (the permeability of free space) is approximately and is the distance from the wire. Since we are looking halfway between the wires, (5 cm).

For both wires (let’s call them Wire 1 and Wire 2), the currents are equal at but in opposite directions. Thus, the magnetic fields due to each wire will be equal in magnitude but opposite in direction halfway between the wires. Therefore, they will cancel each other out, leaving the net magnetic field as zero:

The answer is (D) Zero.

Now let’s dive into some background and applications of these concepts!

The magnetic field produced by an electric current was first discovered by Hans Christian Ørsted in 1820, and this groundbreaking finding laid the groundwork for electromagnetism. The directional nature of the magnetic field due to current-carrying wires is dictated by the right-hand rule, which helps visualize how the fields interact.

In the real world, this principle is critical in designing circuit layouts and understanding how devices like electric motors work. When engineers need to manage electromagnetic interference in circuit boards, the understanding of how magnetic fields interact in parallel wires helps them make safer and more efficient designs.