Two long, straight parallel wires are 10.0 cm apart and carry 4.00 A currents in the same direct

step 1 In the given problem, there are two straight parallel current carrying conductors of infinite le

Two long, straight parallel wires are 10.0 cm apart and...

Two long, straight parallel wires are 10.0 $\mathrm{cm}$ apart and carry 4.00 $\mathrm{A}$ currents in the same direction (Figure 20.68). Find the magnitude and direction of the magnetic field at (a) point $P_{1}$ midway between the wires, (b) point $P_{2}, 25.0 \mathrm{cm}$ to the right of $P_{1}$

Key Concepts

Magnetic Field from a Long Straight Wire

This concept involves the determination of the magnetic field generated by a current-carrying wire, which is given by the formula B = (?? I)/(2?r). This relationship, derived from the Biot–Savart law or Ampère’s law, shows that the magnetic field’s magnitude is directly proportional to the current and inversely proportional to the distance from the wire, making it fundamental in solving problems involving magnetic fields due to currents.

Right-Hand Rule

The right-hand rule is used to determine the direction of the magnetic field around a current-carrying conductor. By pointing the thumb of the right hand in the direction of the current, the curled fingers indicate the direction in which the magnetic field circulates. This rule is crucial for analyzing the vector nature of magnetic fields in problems with multiple current sources.

Superposition Principle

In magnetic field problems involving more than one current-carrying wire, the superposition principle is applied to calculate the resultant magnetic field by summing the individual fields vectorially. Since magnetic fields are vectors, both magnitude and direction must be considered, and contributions from different sources are added according to their orientation and magnitudes.

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