force between two current carrying straight wire // how to get direction of force on each of them

#class_12_physics #physics #cbse_12th_class The force between two current-carrying straight wires can be calculated using the following formula: F = (μ₀ / 4π) * (I₁ * I₂ * L) / d where: F = force between the two wires μ₀ = the permeability of free space (4π x 10^-7 N/A^2) I₁, I₂ = the currents flowing through the wires L = the length of the wires d = the distance between the wires To determine the direction of the force on each wire, you can use the right-hand rule. Imagine grasping one wire in your right hand with your fingers pointing in the direction of the current flow. If you curl your fingers towards the other wire, your thumb will point in the direction of the force on that wire. Repeat the same process with the other wire to determine the direction of the force on that wire. Alternatively, you can use the following rule: If the currents in the two wires are in the same direction, the wires will be attracted to each other. If the currents in the two wires are in opposite directions, the wires will repel each other. FULL DERIVATION :- The force between two current-carrying straight wires can be derived from the Biot-Savart Law and the Lorentz force law. The current I₁ in the first wire produces a magnetic field B at a distance r from the wire, given by the Biot-Savart Law: d𝐵 = μ₀/(4π) * I₁ d𝐿 × 𝑟̂ / r² where 𝑟̂ is the unit vector in the radial direction, and d𝐿 is a small length element of the first wire. The magnetic field B exerts a force on the current I₂ in the second wire, given by the Lorentz force law: d𝐹 = I₂ d𝐿 × (𝐵 × 𝑙̂) where 𝑙̂ is the unit vector in the direction of the current I₂. Using the vector triple product, we can write the Lorentz force as: d𝐹 = I₁ I₂ d𝐿₁ × d𝐿₂ × 𝑟̂ / r² where d𝐿₁ and d𝐿₂ are small length elements of the first and second wires, respectively. The total force F between the two wires is the vector sum of all the elemental forces: F = ∫d𝐹 = μ₀/(4π) * I₁ I₂ ∫∫(d𝐿₁ × d𝐿₂) × 𝑟̂ / r² Integrating over the lengths of the two wires, we get: F = μ₀/(4π) * I₁ I₂ L / d where L is the length of the wires. The direction of the force on each wire can be determined using the right-hand rule, as explained in the previous answer.