Two short bar magnets have their magnetic moments 1.2Am² and1.0 Am². They are placed on a horizontal table parallel to each other at a distance of 20 cm between their centers, such that their north poles pointing towards geographic south. They have common magnetic equatorial line. Horizontal component of earth's field is 3.6 * 10 ^ - 5 * T T.then,the resultant horizontal magnetic induction at mid-point of the line joining their centers

Explanation

Recognize the situation:The problem deals with two short bar magnets placed on a horizontal table with their north poles pointing towards the geographic south. They have a common magnetic equator and are separated by a distance of 20.0 cm.Apply the principle of superposition:Since the magnets are placed close together, we can use the principle of superposition to find the resultant magnetic field at the midpoint. This principle states that the magnetic field produced by a combination of magnets is the vector sum of the individual magnetic fields produced by each magnet.Consider the direction of the magnetic fields:Both magnets have their north poles pointing towards the geographic south. By convention, the magnetic field lines point out of a north pole and into a south pole. Therefore, at the midpoint between the magnets, the horizontal components of the magnetic fields produced by both magnets will add up because they are in the same direction.Calculate the individual magnetic fields:The magnetic field produced by a short bar magnet at a point along its axis can be approximated by the formula:B = (μ * 2 * π) / (4π * μ₀ * d)where:B is the magnetic field strength (T)μ is the magnetic moment (Am²)d is the distance from the midpoint of the magnet to the point (m)μ₀ is the permeability of free space (4π x 10^-7 Tm/A)In this case, both magnets have the same magnetic moment (μ₁ = μ₂). Let's denote the distance from the midpoint to the centre of each magnet as 'd' (which is half of the separation distance, d = 0.1 m).Calculate the resultant horizontal magnetic field:As mentioned earlier, the horizontal components of the magnetic fields produced by both magnets add up at the midpoint. Therefore, the resultant horizontal magnetic field (B_res) is:B_res = B₁_horizontal + B₂_horizontalSince the magnetic fields are directed along the horizontal axis, we can directly add their magnitudes:B_res = (μ₁ * 2 * π) / (4π * μ₀ * d) + (μ₂ * 2 * π) / (4π * μ₀ * d)B_res = (μ₁ + μ₂) * 2 * π / (4π * μ₀ * d)Plugging in the known values:B_res = (1.2 Am² + 1.0 Am²) * 2 * π / (4π * 4π x 10^-7 Tm/A * 0.1 m)B_res ≈ 2.56 x 10^-4 TTherefore, the resultant horizontal magnetic induction at the midpoint is 2.56 x 10^-4 T, which corresponds to answer choice C