The question pertains to calculating the current in each of two long parallel conductors placed 10 cm apart, where one conductor carries twice the current of the other and the force between them is 15 kg/metre. Using Ampère's law, the force can be expressed in terms of current and the known constants, allowing for the determination of the individual currents when one is known to be twice the other.
The force between two long parallel conductors can be calculated using Ampère's force law, which states that the force per unit length between two parallel currents I1 and I2, separated by a distance r in vacuum is given by
F/L = (μ0/(2π)) * (I1I2/r), where μ0 is the permeability of free space (μ0 = 4π x 10-7 N/A2).
In the given problem, we have a force of 15 kg/metre between the conductors, which should be converted to newtons (since 1 kg ≈ 9.8 N) and the distance between them is 10 cm (or 0.1 meters). Therefore, we are looking for currents I1 and I2 such that one is twice the other (I2 = 2I1), and together they produce this force. By plugging in the known values into the formula and solving the system of equations, we can find the currents in each conductor.