Two long, straight wires, each with a current of 12.0 A, are placed on two corners of an equilat

step 1 In this question we are given two identical currents at vertices of an equilateral triangle and

Two long, straight wires, each with a current of 12.0 A, are...

Two long, straight wires, each with a current of $12.0 \mathrm{A},$ are placed on two corners of an equilateral triangle with sides of length $2.50 \mathrm{cm}$ as shown. Both of the wires have a current into the page. (a) What is the magnetic field at the third corner of the triangle? (b) Another wire is placed at the third corner, parallel to the other two wires. In which direction should current flow in the third wire so that the force on it is in the $+y$ -direction?

Two long, straight wires, each with a current of $12.0 \mathrm{A},$ are placed on two corners of an equilateral triangle with sides of length $2.50 \mathrm{cm}$ as shown. Both of the wires have a current into the page.
(a) What is the magnetic field at the third corner of the triangle? (b) Another wire is placed at the third corner, parallel to the other two wires. In which direction should current flow in the third wire so that the force on it is in the $+y$ -direction?

Key Concepts

Right-Hand Rule for Magnetic Fields

The right-hand rule is a mnemonic used to determine the direction of the magnetic field produced by a current. For a long straight conductor, if the thumb points in the direction of the current, the curl of the fingers shows the direction of the magnetic field lines encircling the wire.

Magnetic Force on a Current-Carrying Conductor

A current-carrying conductor in an external magnetic field experiences a force given by F = I(L × B), where L is the vector length in the direction of the current and B is the magnetic field. The direction of this force is determined using the right-hand rule applied to the cross product of L and B, which is essential for predicting how the conductor will interact with the magnetic field.

Superposition Principle for Magnetic Fields

The superposition principle states that magnetic fields from multiple sources add vectorially. When multiple current-carrying wires produce magnetic fields at a point in space, the net magnetic field is the vector sum of the individual fields, taking both magnitude and direction into account.

Magnetic Field of a Long Straight Conductor

A fundamental concept in electromagnetism is that a long, straight current-carrying conductor produces a magnetic field around it, whose magnitude at a distance r is given by B = ??I/(2?r). This formula is derived from the Biot–Savart Law and helps determine how the strength of the magnetic field falls off with distance from the wire.

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