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Phy's 1402 Hw #4 R Sliding bar a) Find the Costat Kat By the battery in tHe Cirlunt. dejver b) G:Ven that dd CaSTent, Find the Mgatade of the force on the Sliding Bas. Now imgine that the sliding bar hoaa Mass CM). what is the accelaation of the Sliding bar?

Phy's 1402 Hw #4 R Sliding bar a) Find the Costat Kat By the battery in tHe Cirlunt. dejver b) G:Ven that dd CaSTent, Find the Mgatade of the force on the Sliding Bas. Now imgine that the sliding bar hoaa Mass CM). what is the accelaation of the Sliding bar?

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**Physics 1402 - Homework #4** **1. [Diagram Description]** The diagram consists of a circuit with a battery (voltage \( \mathcal{E} \)), a resistor \( R \), and a sliding bar between points \( B \) and \( D \). There is an inductor \( M \) in the system. **Questions:** a) Find the current \( I \) delivered by the battery in the circuit. b) Given that induced current, find the magnitude of the force on the sliding bar. c) Now imagine that the sliding bar has a mass \( m \). What is the acceleration of the sliding bar? d) After a time \( t \), what is the speed of the sliding bar? (Assume it started from rest and that the acceleration is constant.) e) Find the induced EMF caused by the motion of the sliding bar. f) Find the magnitude of the total current in the circuit. (The induced current will be in the opposite direction to the battery-driven current.) g) Show that the total current can be written as the battery-driven current times an efficiency factor. h) Show that the force on the sliding bar can be written as the force from part (b) times the efficiency factor in part (g). **2. Physics 1402 - Homework #4** Consider two conducting rings with radii \( R_1 \) and \( R_2 \) respectively. The rings share the same central axis and their centers are separated by a distance \( D \). If \( R_1 > \gg R_2 \), find the following: a) \( M_{21} = ? \) (Note: The question involves calculating mutual inductance between two rings based on the given parameters.)
Transcribed Image Text:**Physics 1402 - Homework #4** **1. [Diagram Description]** The diagram consists of a circuit with a battery (voltage \( \mathcal{E} \)), a resistor \( R \), and a sliding bar between points \( B \) and \( D \). There is an inductor \( M \) in the system. **Questions:** a) Find the current \( I \) delivered by the battery in the circuit. b) Given that induced current, find the magnitude of the force on the sliding bar. c) Now imagine that the sliding bar has a mass \( m \). What is the acceleration of the sliding bar? d) After a time \( t \), what is the speed of the sliding bar? (Assume it started from rest and that the acceleration is constant.) e) Find the induced EMF caused by the motion of the sliding bar. f) Find the magnitude of the total current in the circuit. (The induced current will be in the opposite direction to the battery-driven current.) g) Show that the total current can be written as the battery-driven current times an efficiency factor. h) Show that the force on the sliding bar can be written as the force from part (b) times the efficiency factor in part (g). **2. Physics 1402 - Homework #4** Consider two conducting rings with radii \( R_1 \) and \( R_2 \) respectively. The rings share the same central axis and their centers are separated by a distance \( D \). If \( R_1 > \gg R_2 \), find the following: a) \( M_{21} = ? \) (Note: The question involves calculating mutual inductance between two rings based on the given parameters.)
Expert Solution
Step 1 To determine,

(i)The current driven by the battery in the circuit.

(ii) magnitude of the force on the sliding bar.

(iii) The acceleration of the sliding bar, if the mass of the sliding bar is m.

Given,

battery potential=εresistance of the wire=Rmagnetic field=B ⊗

 

 

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