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... CPA circular coil with N1 = 5000 turns is made of a conducting material with resistance 0.0100 2/m and radius a = 40.0 cm. The coil is attached to a C = 10.00 uF capacitor as shown in Fig. P29.600. A second coil with radius b= 4.00 cm, made of the same wire, with Na = 100 turns, is concentric with the first coil and parallel to it. The capacitor has a charge of +100 uC on its upper plate, and the switch S is open. At time t =0 the switch is closed. (a) What is the magnitude of the current in the larger coil immediately after the switch is closed? (b) What is the magnetic flux through each turn of the smaller coil immediately after the switch is closed? (Since b a, we may treat the magnetic field in the smaller coil due to the larger coil as uniform.) (c) What is the direction of the current in the smaller coil immediately after the switch is closed? (d) What is the direction of the current in the

... CPA circular coil with N1 = 5000 turns is made of a conducting material with resistance 0.0100 2/m and radius a = 40.0 cm. The coil is attached to a C = 10.00 uF capacitor as shown in Fig. P29.600. A second coil with radius b= 4.00 cm, made of the same wire, with Na = 100 turns, is concentric with the first coil and parallel to it. The capacitor has a charge of +100 uC on its upper plate, and the switch S is open. At time t =0 the switch is closed. (a) What is the magnitude of the current in the larger coil immediately after the switch is closed? (b) What is the magnetic flux through each turn of the smaller coil immediately after the switch is closed? (Since b a, we may treat the magnetic field in the smaller coil due to the larger coil as uniform.) (c) What is the direction of the current in the smaller coil immediately after the switch is closed? (d) What is the direction of the current in the

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## Problem 5 **Context:** A circular coil with \( N_1 = 5000 \) turns is made of a conducting material with a resistance of \( 0.0100 \, \Omega/\text{m} \) and a radius \( a = 40.0 \, \text{cm} \). The coil is connected to a \( C = 10.00 \, \mu\text{F} \) capacitor as shown in Fig. P29.60P. A second coil with a radius \( b = 4.00 \, \text{cm} \), made of the same material, with \( N_2 = 100 \) turns, is concentric with the first coil and parallel to it. The capacitor has a charge of \( +100 \, \mu\text{C} \) on its upper plate, and the switch \( S \) is open. **At time \( t = 0 \),** the switch is closed. ### Sub-questions: a) What is the magnitude of the current in the larger coil immediately after the switch is closed? b) What is the magnetic flux through each turn of the smaller coil immediately after the switch is closed? (Given that since part b is related to part a, the magnetic field in the smaller coil due to the larger coil is uniform.) c) What is the direction of the current in the smaller coil immediately after the switch is closed? d) What is the direction of the current in the smaller coil at \( t = 1.26 \, \text{ms}? \) e) What is the magnitude of the current in the smaller coil at \( t = 1.26 \, \text{ms}? \) **Explanation:** To solve these questions, one needs to apply the principles of electromagnetic induction, Ohm's law, and Kirchhoff's voltage laws. The key steps would typically involve computing the initial current using the charge on the capacitor, determining the resulting magnetic field, calculating the induced emf in the smaller coil, and using Lenz's law to find the direction of the induced current. ### Diagram Explanation: In the given figure (Fig. P29.60P), we likely see two concentric circular coils, one with a much larger radius than the other, connected by a switch and a capacitor. The larger coil probably surrounds the smaller coil, which allows the induced magnetic field
Transcribed Image Text:## Problem 5 **Context:** A circular coil with \( N_1 = 5000 \) turns is made of a conducting material with a resistance of \( 0.0100 \, \Omega/\text{m} \) and a radius \( a = 40.0 \, \text{cm} \). The coil is connected to a \( C = 10.00 \, \mu\text{F} \) capacitor as shown in Fig. P29.60P. A second coil with a radius \( b = 4.00 \, \text{cm} \), made of the same material, with \( N_2 = 100 \) turns, is concentric with the first coil and parallel to it. The capacitor has a charge of \( +100 \, \mu\text{C} \) on its upper plate, and the switch \( S \) is open. **At time \( t = 0 \),** the switch is closed. ### Sub-questions: a) What is the magnitude of the current in the larger coil immediately after the switch is closed? b) What is the magnetic flux through each turn of the smaller coil immediately after the switch is closed? (Given that since part b is related to part a, the magnetic field in the smaller coil due to the larger coil is uniform.) c) What is the direction of the current in the smaller coil immediately after the switch is closed? d) What is the direction of the current in the smaller coil at \( t = 1.26 \, \text{ms}? \) e) What is the magnitude of the current in the smaller coil at \( t = 1.26 \, \text{ms}? \) **Explanation:** To solve these questions, one needs to apply the principles of electromagnetic induction, Ohm's law, and Kirchhoff's voltage laws. The key steps would typically involve computing the initial current using the charge on the capacitor, determining the resulting magnetic field, calculating the induced emf in the smaller coil, and using Lenz's law to find the direction of the induced current. ### Diagram Explanation: In the given figure (Fig. P29.60P), we likely see two concentric circular coils, one with a much larger radius than the other, connected by a switch and a capacitor. The larger coil probably surrounds the smaller coil, which allows the induced magnetic field
**Problem Description and Graphical Analysis** In the provided problem, we are given a coil with turns \(N_1\) and \(N_2\), and dimensions \(2b\) and \(a\) respectively. Attached to the coil is a switch \(S\) and a capacitor \(C\). The task requires us to analyze this setup and provide graphs for \( q(t) \) and \( i(t) \), where \( q(t) \) represents the charge as a function of time, and \( i(t) \) represents the current as a function of time. ### Diagram Analysis The given diagram depicts an electrical circuit element consisting of: - \(N_1\) turns of wire forming one coil. - \(N_2\) turns of wire forming another coil. - A switch \(S\) which is presumably used to open or close the circuit. - A capacitor \(C\) which stores electrical energy. - The distance \(2b\) representing the horizontal span of the coil. - The distance \(a\) indicating the separation between the coils. ### Additional Questions 1. **Graphical Representation of \( q(t) \) and \( i(t) \)** - **\( q(t) \)**: Plot the charge stored in the capacitor over time. This may show how the capacitor charges and discharges when the switch \(S\) is operated. - **\( i(t) \)**: Plot the current flowing through the circuit as a function of time. This graph will typically display transient behaviors such as exponential rise or decay, based on the inductance of the coils and the capacitance of the capacitor. Using these graphs, quantitatively evaluate the solution for the given problem by analyzing parameters like peak charge, time constants, and current amplitudes. This analysis will help in understanding the dynamic response of the RC (Resistor-Capacitor) circuit in conjunction with the inductor coils. **Note:** To thoroughly solve this problem, apply principles of electromagnetism and circuit theory, including Kirchhoff's laws and the equations governing RC circuits and inductance.
Transcribed Image Text:**Problem Description and Graphical Analysis** In the provided problem, we are given a coil with turns \(N_1\) and \(N_2\), and dimensions \(2b\) and \(a\) respectively. Attached to the coil is a switch \(S\) and a capacitor \(C\). The task requires us to analyze this setup and provide graphs for \( q(t) \) and \( i(t) \), where \( q(t) \) represents the charge as a function of time, and \( i(t) \) represents the current as a function of time. ### Diagram Analysis The given diagram depicts an electrical circuit element consisting of: - \(N_1\) turns of wire forming one coil. - \(N_2\) turns of wire forming another coil. - A switch \(S\) which is presumably used to open or close the circuit. - A capacitor \(C\) which stores electrical energy. - The distance \(2b\) representing the horizontal span of the coil. - The distance \(a\) indicating the separation between the coils. ### Additional Questions 1. **Graphical Representation of \( q(t) \) and \( i(t) \)** - **\( q(t) \)**: Plot the charge stored in the capacitor over time. This may show how the capacitor charges and discharges when the switch \(S\) is operated. - **\( i(t) \)**: Plot the current flowing through the circuit as a function of time. This graph will typically display transient behaviors such as exponential rise or decay, based on the inductance of the coils and the capacitance of the capacitor. Using these graphs, quantitatively evaluate the solution for the given problem by analyzing parameters like peak charge, time constants, and current amplitudes. This analysis will help in understanding the dynamic response of the RC (Resistor-Capacitor) circuit in conjunction with the inductor coils. **Note:** To thoroughly solve this problem, apply principles of electromagnetism and circuit theory, including Kirchhoff's laws and the equations governing RC circuits and inductance.
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