A rectangular loop of wire, carrying current I1=2.0 mA, is next to a very long wire carrying a c

step 1 Hi, in the given problem, first of all there is a long straight current carrying conductor which

A rectangular loop of wire, carrying current I1=2.0 mA, is...

A rectangular loop of wire, carrying current $I_{1}=2.0 \mathrm{mA},$ is next to a very long wire carrying a current $I_{2}=8.0$ A. (a) What is the direction of the magnetic force on each of the four sides of the rectangle due to the long wire's magnetic field? (b) Calculate the net magnetic force on the rectangular loop due to the long wire's magnetic field. [Hint: The long wire does not produce a uniform magnetic field.] (c) What is the magnetic force on the long wire due to the loop?

A rectangular loop of wire, carrying current $I_{1}=2.0 \mathrm{mA},$ is next to a very long wire carrying a current $I_{2}=8.0$ A. (a) What is the direction of the magnetic force on each of the four sides of the rectangle due to the long wire's magnetic field?
(b) Calculate the net magnetic force on the rectangular loop due to the long wire's magnetic field. [Hint: The long wire does not produce a uniform magnetic field.] (c) What is the magnetic force on the long wire due to the loop?

Key Concepts

Newton’s Third Law in Magnetism

Newton’s Third Law states that for every action, there is an equal and opposite reaction. This principle applies in electromagnetic interactions as well, meaning the force exerted by a current-carrying loop on a long wire is equal in magnitude and opposite in direction to the force exerted by the long wire on the current loop. This principle is key to analyzing the mutual interactions between different current-carrying elements.

Right-Hand Rule for Magnetic Interactions

The right-hand rule is a mnemonic for determining the direction of the magnetic field generated by a current, as well as the direction of the force experienced by a current-carrying conductor within a magnetic field. When applied to the force on a current element, it involves pointing the fingers in the direction of the current and curling them towards the direction of the magnetic field; the thumb then points in the direction of the resulting force.

Magnetic Force on a Current-Carrying Conductor

A current-carrying conductor in an external magnetic field experiences a force described by the Lorentz or magnetic force law, F = I (L × B), where I is the current, L is the length vector of the conductor segment, and B is the magnetic field. The magnitude and direction of this force depend on both the orientation of the current-carrying segment and the local magnetic field, leading to different forces on different sides of a current loop when the field is non-uniform.

Magnetic Field Due to a Current-Carrying Wire

A current-carrying wire generates a magnetic field that circulates around the wire. The magnitude of the magnetic field decreases with distance from the wire (typically following an inverse relationship with radius), and its direction is given by the right-hand rule. This concept is essential to understanding how nearby conductors, such as the sides of a rectangular loop, experience different magnetic field strengths depending on their proximity to the wire.

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