Question

For parallel conductors and steady currents, the results in accordan with Newton's third law are

• A. Biot-Savart law and the Lorentz force
• B. Biot-Savart law and Ampere's law
• C. Ampere's law and the Lorentz force
• D. Lenz's law and Lorentz force

Hint:

Force Between Currents:

• Biot–Savart: $d\vecB = \frac\mu_04\pi \cdot \fracId\vecl \times \hatrr^2$
• Lorentz Force: $\vecF = I \vecl \times \vecB$
• For parallel wires: $F \propto \dfracI_1 I_2d$

Answer 1

The Correct Option is A

To derive mutual force between wires:

• Use Biot-Savart law to find magnetic field from one wire.
• Use Lorentz force to find force on second wire due to that field.

This force turns out to be equal and opposite, thus satisfying Newton's third law.

Answer 2

Step 1: Understand the context
When two parallel conductors carry steady currents, they exert forces on each other.
These forces arise due to the magnetic fields produced by the currents.

Step 2: Biot-Savart law
The Biot-Savart law helps calculate the magnetic field \( \vec{B} \) produced at a point due to a small segment of current-carrying conductor.
For a long straight conductor carrying current \( I \), the magnetic field at a distance \( r \) is:
\[ B = \frac{\mu_0 I}{2\pi r} \]

Step 3: Lorentz force law
The force on a current-carrying conductor in a magnetic field is given by the Lorentz force:
\[ \vec{F} = I \vec{L} \times \vec{B} \]
where \( \vec{L} \) is the length vector of the conductor.

Step 4: Newton’s third law in this context
The forces between the two conductors are equal in magnitude and opposite in direction, satisfying Newton's third law.
Using the Biot-Savart law to find the magnetic field and the Lorentz force to find the force on the other conductor explains this mutual interaction.

Step 5: Conclusion
Hence, the correct theoretical framework that explains the forces between parallel conductors in accordance with Newton’s third law involves the Biot-Savart law and the Lorentz force.