A magnetic needle is disposed inside a horizontal coil. In the abscence of any electric current the needle is observed to get oriented in a direction perpendicular to the x'x of the coil.

a) what is the direction of the terrestrial magnetic field.
b) A current I is allowed in the coil the magnetic needle deviates through an angle alpha.
Determine the direction of the current in the coil.
Calculate the intensity of the magnetic field created by the coil

To determine the direction of the terrestrial magnetic field, you would need a reference point or information about the location where the experiment is conducted. However, assuming the experiment is conducted on Earth, the terrestrial magnetic field generally points from the geographic south to the geographic north.

To determine the direction of the current in the coil and the intensity of the magnetic field created by the coil, you can apply Ampere's Law. Ampere's Law states that the magnetic field created by a current-carrying conductor is directly proportional to the current and inversely proportional to the distance from the conductor.

Here's how you can proceed:

Step 1: Determine the orientation of the magnetic needle when a current is flowing through the coil. From the given information, the needle deviates through an angle alpha. If the angle of deviation is towards the direction of the geographic north, then the current must be flowing anticlockwise when observed from above the coil. If the angle of deviation is towards the direction of the geographic south, then the current must be flowing clockwise.

Step 2: Once you determine the direction of the current flow, you can establish a right-hand rule to determine the direction of the magnetic field created by the coil. Point your right thumb in the direction of the current flow (anticlockwise or clockwise) when observed from above the coil, and your fingers will curl in the direction of the magnetic field lines.

Step 3: To calculate the intensity of the magnetic field created by the coil, you can use the formula:
B = (μ₀ * I) / (2 * π * r)
where B is the magnetic field, μ₀ is the permeability of free space (constant value), I is the current flowing through the coil, and r is the distance from the center of the coil to the point where you want to measure the magnetic field.

By substituting the values of μ₀, I, and r into the formula, you can calculate the intensity of the magnetic field created by the coil.

Remember, the above steps are based on the assumptions and given information. In a practical scenario, it is essential to consider other factors and measurements to obtain accurate results.