1. A circular metal ring is placed inside an air-core solenoid as in Fig. 1. It is held in place by unseen, plastic brackets. The solenoid is connected to a D.C. power supply which creates a spatially uniform (primary) magnetic field inside the solenoid. In Fig. 2 the primary magnetic field is drawn as the array of dots. The solenoid has 11,300 turns of wire and is 35.5 cm long. The power supply connected to the solenoid is programmed to increase the current in the solenoid according to: I(t) = 0.200t Amp. The radius of the ring is a = 10.0 cm and it has a resistance of 1.571 Ohm. a. Determine an expression for the magnitude of the primary magnetic field inside the solenoid as a function of time. b. Determine the direction of the induced current in the ring. c. Calculate the size of the induced EMF in the ring. A ())) Fig. 1 Fig. 2 Y 8
1. A circular metal ring is placed inside an air-core solenoid as in Fig. 1. It is held in place by unseen, plastic brackets. The solenoid is connected to a D.C. power supply which creates a spatially uniform (primary) magnetic field inside the solenoid. In Fig. 2 the primary magnetic field is drawn as the array of dots. The solenoid has 11,300 turns of wire and is 35.5 cm long. The power supply connected to the solenoid is programmed to increase the current in the solenoid according to: I(t) = 0.200t Amp. The radius of the ring is a = 10.0 cm and it has a resistance of 1.571 Ohm. a. Determine an expression for the magnitude of the primary magnetic field inside the solenoid as a function of time. b. Determine the direction of the induced current in the ring. c. Calculate the size of the induced EMF in the ring. A ())) Fig. 1 Fig. 2 Y 8
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Transcribed Image Text:**Problem Statement:**
A circular metal ring is placed inside an air-core solenoid as shown in Fig. 1. It is held in place by unseen, plastic brackets. The solenoid is connected to a D.C. power supply which creates a spatially uniform (primary) magnetic field inside the solenoid. In Fig. 2, the primary magnetic field is represented by an array of dots. The solenoid has 11,300 turns of wire and is 35.5 cm long. The power supply connected to the solenoid is programmed to increase the current in the solenoid according to: \( I(t) = 0.200t \) Amp. The radius of the ring is \( a = 10.0 \) cm and it has a resistance of 1.571 Ohm.
**Questions:**
a. Determine an expression for the magnitude of the primary magnetic field inside the solenoid as a function of time.
b. Determine the direction of the induced current in the ring.
c. Calculate the size of the induced EMF in the ring.
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**Figures Explained:**
*Figure 1:* A cylindrical solenoid is depicted with the axis labeled as \( z \). A circular metal ring is positioned horizontally inside the solenoid. The spatial arrangement reflects the relationship between the solenoid and the ring within the three-dimensional \( xyz \)-coordinate system.
*Figure 2:* A top-down view (cross-section) of the solenoid shows the circular metal ring. The magnetic field is symbolized by dots, indicating a uniform field perpendicular to the plane of the ring. A coordinate system is overlaid with axes marked \( x \) and \( y \), and the radius of the ring is denoted by \( a \).
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