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(Solved): The figure below shows an end view of a single-turn square loop of metal wire in the center of and ...
The figure below shows an end view of a single-turn square loop of metal wire in the center of and coaxial with a very long solenoid with a circular cross section. The solenoid is long, has a radius , and consists of 124 turns of wire. The length of each side of the square loop is . (a) The current in the solenoid is . What is the magnetic flux through the square loop in ? What is the formula for the magnetic field of a solenoid? What area should you use to calculate the flux through the loop? Be careful of unit conversions. (b) The current decreases from to zero in . What is the magnitude of the average induced emf in the square loop (in V) over this time?
Expert Answer
A solenoid's magnetic field is determined by:a=B = ???N?I / LwhereThe permeability of empty space is zero (4 10-7 Tm/A).N is the solenoid's number of turns.I represents the solenoid's current.L is the solenoid's length.The square loop's surface area is:A = ?² = (1.50 cm)² = 2.25 cm² = 2.25 × m²The square loop's magnetic flux measures as follows:? = B?A= ???N?I / L?A= ???N?I / L?2.25 × 10-4 m²= (4 × 10-7 T?m/A)?124?2.00 A / 15.0 cm?2.25 × 10-4 m²= 1.13 T?m²