Question

Two long, straight, parallel wires are separated by a distance of 6.00 cm. One wire carries a current of 1.45 A, the other carries a current of 4.34 A in the same direction. Calculate the strength of the magnetic field halfway between the wires, in microteslas.

Answer 1

56.1 microteslas

Step-by-step explanation:

We have two parallel wires separated by 6.00 cm. One wire carries a current of 1.45 A and the other carries 4.34 A in the same direction.

According to the Biot-Savart law, the magnetic field produced by a long straight current-carrying wire at a point on its axis is given by:

⇒ B = (μo/2π)*I/r

Where:

• B is the magnetic field strength
• μo is the permeability of free space = 4π x 10^-7 Tm/A
• I is the current in the wire
• r is the distance from the wire

Since the wires are carrying current in the same direction, their magnetic fields will add. We can calculate the total magnetic field as:

⇒ Btotal = B1 + B2

⇒ = (μo/2π)(I1/r) + (μo/2π)(I2/r)

Where I1 = 1.45 A and I2 = 4.34 A are the currents, and

⇒ r = 0.06 m is the distance (half the 6 cm separation)

Substituting the given values into the equation yields:

⇒ Btotal = (4πx10^-7)(1.45/(0.06)) + (4πx10^-7)(4.34/(0.06))

= 56.1 μT

Therefore, the strength of the magnetic field halfway between the wires is 56.1 microteslas.

Answer 2

magnetic field halfway between the wires is 17.833 microteslas.

Step-by-step explanation:

B1 = (μ₀ * I1) / (2 * π * r)

where B1 is the magnetic field due to the wire with current I1

B2 = (μ₀ * I2) / (2 * π * r)

where B2 is the magnetic field due to the wire with current I2.

so

B_total=B1+B2

Substituting the given values, i have:

B1 = (4π × 10^-7 T·m/A * 1.45 A) / (2 * π * 0.06 m)

B1 = (2 × 10^-7 T) / 0.06

B1 = 3.33 × 10^-6 T

B2 = (4π × 10^-7 T·m/A * 4.34 A) / (2 * π * 0.06 m)

B2 = (8.68 × 10^-7 T) / 0.06

B2 = 1.45 × 10^-5 T

B_total = B1 + B2

B_total = 3.33 × 10^-6 T + 1.45 × 10^-5 T

B_total = 1.7833 × 10^-5 T

To express the magnetic field strength in microteslas, we multiply by 10^6:

B_total = 1.7833 × 10^-5 T * 10^6

B_total = 17.833 μT

I hope this is correct and it works for you