Question

A long, straight, conducting wire carries a current of 2.00 A. A second, identical wire is parallel to the first and separated from it by 3.50 cm. The magnetic field at a point halfway between the two wires has magnitude 6.00×10^−5

T. What is the current in the second wire if its direction is the same as in the first wire? Express your answer with the appropriate units. (1) You have already submitted this answer. Enter a new answer. No credit lost. Try again. Part F What is the current in the second wire if its direction is opposite to that in the first wire? Express your answer with the appropriate units.

Answer 1

The current in the second wire is 2.00 A, whether it is in the same or opposite direction as the current in the first wire, because the magnetic fields produced by the wires add vectorially, leading to the observed net magnetic field at the midpoint.

Step-by-step explanation:

The magnetic field created by a long, straight, conducting wire can be calculated using Ampère's law. The magnetic field at a point due to a current-carrying wire is directly proportional to the current and inversely proportional to the distance from the wire. When there are two wires with current flowing in the same or opposite directions, their magnetic fields add vectorially.

For two parallel currents flowing in the same direction, the magnetic fields due to each wire at the midpoint will be in opposite directions. They will subtract from each other, resulting in a net magnetic field lower than that created by a single wire. Conversely, if the currents are in opposite directions, the magnetic fields at the midpoint will add up.

To solve part (1) of the student's question, we assume the currents are in the same direction. Using the Biot-Savart Law or Ampère's Law, we find that the individual magnetic fields due to each wire must be 3.00 × 10−5 T to create a net field of 6.00 × 10−5 T at the midpoint, implying the currents are equal. Therefore, the second wire also carries a current of 2.00 A.

For part (F), with the currents in opposite directions, the net magnetic field will be the sum of the individual fields from the two wires. Since the net field is 6.00 × 10−5 T, produced by the original wire's 2.00 A current, the current in the second wire must be such that its magnetic field is equal in magnitude and opposite in direction to the first, yielding the same 2.00 A but opposite in direction to maintain the net field at the same magnitude.