Final answer:
The question involves comparing the magnetic field of a finite solenoid to that of the infinite approximation, and whether it is a good approximation. An infinite solenoid is presumed to have a uniform magnetic field inside and nearly zero outside, excluding the ends. Values for actual measurements are necessary to solve the mathematical problem and determine the exact net magnetic field strength.
Step-by-step explanation:
The student question asks about the similarity between a short solenoid and an infinite solenoid, and whether the approximation of an infinite solenoid is acceptable for calculating the magnetic field outside a short solenoid. In physics, particularly electromagnetism, the concept of an infinite solenoid is used to simplify calculations by assuming the magnetic field is uniform inside and effectively zero outside, except near the ends.
This is because the solenoid's length is much larger than its diameter, and so end effects can be ignored. The formula for the magnetic field inside a solenoid is given by B = μ0nI, where B is the magnetic field, μ0 is the magnetic constant or the permeability of free space, n is the number of turns per unit length, and I is the current through the solenoid.
To solve the mathematical problem and give me a 500 word answer regarding the ratio of the magnetic field produced by using a finite formula over the infinite approximation at 85° and 89°, specific values of magnetic field strength would need to be calculated. The given solenoid has 1000 turns in 50 cm with a 1.0 A current. To find the number of turns per unit length, n = 1000 turns / 0.50 m = 2000 turns/m.
With μ0 approximately equal to 1.2566 × 10-6 T·m/A, the magnetic field inside the solenoid can be calculated. To assess the net magnetic field outside the solenoid when current is flowing, it's important to recognize that the approximation of an infinite solenoid generally leads to a near-zero magnetic field outside, however, in practice, the finite solenoid will have some fringe fields at the ends.