The figure below shows an end view of a solenoid along its axis. The solenoid has a circular cross section with a radius of r = 3.00 cm. It consists of 126 turns of wire and is 15.0 cm long. Inside the solenoid, near its center and coaxial with it, is a single loop of wire in the shape of a square, with each side of length ℓ = 1.00 cm. (The plane of the square loop is perpendicular to the solenoid axis.) A square with sides of length ℓ is completely inside of and concentric with a circle of radius r. (a) Initially, there is a steady current of 4.00 A through the solenoid. What is the magnitude of the magnetic flux (in T · m2) through the square loop? T · m2 (b) The current in the solenoid is then reduced from its initial value to zero within 2.00 s. What is the magnitude of the average induced emf (in V) in the square loop during this time? V
The figure below shows an end view of a solenoid along its axis. The solenoid has a circular cross section with a radius of r = 3.00 cm. It consists of 126 turns of wire and is 15.0 cm long. Inside the solenoid, near its center and coaxial with it, is a single loop of wire in the shape of a square, with each side of length ℓ = 1.00 cm. (The plane of the square loop is perpendicular to the solenoid axis.) A square with sides of length ℓ is completely inside of and concentric with a circle of radius r. (a) Initially, there is a steady current of 4.00 A through the solenoid. What is the magnitude of the magnetic flux (in T · m2) through the square loop? T · m2 (b) The current in the solenoid is then reduced from its initial value to zero within 2.00 s. What is the magnitude of the average induced emf (in V) in the square loop during this time? V
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Question
The figure below shows an end view of a solenoid along its axis. The solenoid has a circular cross section with a radius of r = 3.00 cm. It consists of 126 turns of wire and is 15.0 cm long. Inside the solenoid, near its center and coaxial with it, is a single loop of wire in the shape of a square, with each side of length ℓ = 1.00 cm. (The plane of the square loop is perpendicular to the solenoid axis.)
A square with sides of length ℓ is completely inside of and concentric with a circle of radius r.
(a)
Initially, there is a steady current of 4.00 A through the solenoid. What is the magnitude of the magnetic flux (in T · m2) through the square loop?
T · m2
(b)
The current in the solenoid is then reduced from its initial value to zero within 2.00 s. What is the magnitude of the average induced emf (in V) in the square loop during this time?
V
Expert Solution
Step 1
The magnetic field produced by a solenoid lies along the axis of the solenoid, and is given by the equation
Inside this solenoid, is a loop of wire in the form of a square of side 1 cm, co-axial with the solenoid.
As the magnetic field produced by the solenoid lies along the axis of the solenoid, and as the square loop is co-axial to the solenoid, the magnetic field thus also lies along the axis of the square loop
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