This HW is about INDUCTANCE AND LR CIRCUITS, and you can just follow instructions in the word file and type answers in the file.

FARADAYÃ¢â‚¬â„¢S LAW, INDUCTANCE AND LR CIRCUITS

PHYSICS OBJECTIVES AND READINGS

Names:

Physics objectives: The complete list of PHYS 151 course

objectives is on Angel. This assignment focus on

____________________________

1. determining the induced electric field, EMF, and/or

current due to a changing magnetic flux (FaradayÃ¢â‚¬â„¢s

Law and LenzÃ¢â‚¬â„¢s law)

2. describing the behavior of RL circuits.

____________________________

Readings: Knight Chap 33.

____________________________

Useful Equations & Concepts

Ã¢Æ’â€”

The magnetic flux Ã°Ââ€ºÂ·Ã°Ââ€˜Å¡ through an area in a magnetic field Ã°ÂÂÂµ

Ã¢Æ’â€” Ã¢â€¹â€¦ Ã°Ââ€˜â€˜Ã°ÂÂÂ´.

is defined as: Ã°Ââ€ºÂ·Ã°Ââ€˜Å¡ = Ã¢Ë†Â« Ã°ÂÂÂµ

Faraday’s Law of Induction: If the magnetic flux Ã°Ââ€ºÂ·Ã°Ââ€˜Å¡ through a

closed loop C changes with time, an induced electric field Ã°ÂÂÂ¸Ã¢Æ’â€” is

created. The rate of change of the magnetic flux and the

electric field are related by:

Ã¢Ë†Â® Ã°ÂÂÂ¸Ã¢Æ’â€” Ã¢â€¹â€¦ Ã°Ââ€˜â€˜Ã°Ââ€˜Â = Ã¢Ë†â€™

The potential difference across an inductor is Ã°Ââ€ºÂ¥Ã°Ââ€˜â€°Ã°ÂÂÂ¿ = Ã¢Ë†â€™Ã°ÂÂÂ¿

Section #______________

Date: _____________

Ã°Ââ€˜â€˜Ã°Ââ€ºÂ·Ã°Ââ€˜Å¡

Ã°Ââ€˜â€˜Ã°Ââ€˜Â¡

Ã°Ââ€˜â€˜Ã°ÂÂÂ¼

Ã°Ââ€˜â€˜Ã°Ââ€˜Â¡

where L is the inductance of the coil

(inductor). Inductance is measured in units of henries (H). Here are some rules of thumb for RL circuits:

o

When you make a change in an RL circuit, initially, an inductor acts to oppose the change in

current. A long time later, it acts like an ordinary piece of wire.

o

Circuits with inductors resist any changes in current; so, if you throw a switch, the current

through an inductor cannot change instantaneously (unless, there is only an inductor in the

circuits).

The current in series RL circuit is

Rise of current:

Ã°ÂÂÂ¿

Ã¢â€žâ€¡

Ã°ÂÂÂ¼ = Ã°Ââ€˜â€¦ (1 Ã¢Ë†â€™ Ã°Ââ€˜â€™

Ã¢Ë†â€™

Ã°Ââ€˜Â¡

Ã°ÂÅ“ÂÃ°ÂÂÂ¿

)

Decay of current:

Ã°ÂÂÂ¼ = Ã°ÂÂÂ¼0 Ã°Ââ€˜â€™

Ã¢Ë†â€™

Where Ã°ÂÅ“ÂÃ°ÂÂÂ¿ = Ã°Ââ€˜â€¦ . ** Be careful, this is only valid for a circuit with an inductor and a resistor in series.

Ã°Ââ€˜Â¡

Ã°ÂÅ“ÂÃ°ÂÂÂ¿

2

EXERCISE 1: FARADAYÃ¢â‚¬â„¢S LAW AND THE SOLENOID

The figure below shows the cross-sectional view of an ideal solenoid with n turns per unit length and a

Ã°Ââ€˜â€˜Ã°ÂÂÂ¼

radius R1. At some instant in time, the current through the coil is increasing at a rate Ã°Ââ€˜â€˜Ã°Ââ€˜Â¡ and the

instantaneous value of the current is Ã°ÂÂÂ¼ going clockwise as viewed in this picture. A point charge +Q is

located as shown at a distance R2 from the axis of the solenoid.

Looking this way

Ã¢Æ’â€” Ã¢â€¹â€¦ Ã°Ââ€˜â€˜Ã°Ââ€˜Â = Ã°ÂÅ“â€¡0 Ã°ÂÂÂ¼Ã°Ââ€˜Â¡Ã¢â€žÅ½Ã°Ââ€˜Å¸Ã°Ââ€˜Å“Ã°Ââ€˜Â¢Ã°Ââ€˜â€Ã¢â€žÅ½ , we can find the magnetic field in an ideal solenoid to be Ã°ÂÂÂµ =

From AmpÃƒÂ¨reÃ¢â‚¬â„¢s Law Ã¢Ë†Â® Ã°ÂÂÂµ

Ã°ÂÅ“â€¡0 Ã°Ââ€˜â€ºÃ°ÂÂÂ¼ inside and Ã°ÂÂÂµ = 0 outside where Ã°Ââ€˜â€º is the number of coils of wires per unit of length (Ã°Ââ€˜â€º = Ã°Ââ€˜Â/Ã°ÂÂÂ¿). The

direction is found by the right hand rule.

In exercise 1, your aim is to use FaradayÃ¢â‚¬â„¢s Law to determine the instantaneous force experienced by the

charge Q as the current changes.

1. Imagine a circular path of radius R2 concentric with the solenoid. Determine the instantaneous

magnetic flux through the area enclosed by this circle. Calculate the rate of change of this flux

Ã°Ââ€˜â€˜Ã°ÂÂÂ¼

(just the magnitude) given that the current changes and increases at a rate Ã°Ââ€˜â€˜Ã°Ââ€˜Â¡.

3

If you look at the figure again, youÃ¢â‚¬â„¢ll notice that (aside from the charge +Q outside the solenoid), the

entire situation looks exactly the same if you rotate the figure about the center of the solenoid. We say,

then, that the problem is rotationally symmetric. We can use this symmetry to argue that

i)

ii)

the electric field induced by the changing current in the solenoid must be oriented tangent to

any circular path concentric with the solenoid and

the component of the electric field along our imaginary circular path must be constant all

along that circle.

2. So, now that we know from symmetry that the induced electric field must be tangent to our

imaginary circle of radius R2, in which sense is the electric field oriented: clockwise or counterclockwise? One way to answer this is to consider what would happen if there were an actual

conducting wire placed along our imaginary loop. Use LenzÃ¢â‚¬â„¢ law to figure out the direction of the

current that would be induced if you did this, and from this, determine the direction of the

electric field.

3. Given that the magnitude of the electric field must be the same at every point along this

imaginary loop, use the results you have obtained so far to finally determine the instantaneous

force on the point charge Q.

4

R1

EXERCISE 2: LR CIRCUITS

In the circuit shown adjacent, V = 60.0 V, R1 = 10.0 Ã¢â€žÂ¦, R2 = 20.0 Ã¢â€žÂ¦,

and L = 3 H.

+

V

4. Immediately after the switch is closed (right after current

starts flowing), what is the value of the current through

R2? Make sure you justify your answer. Hint: with this

switch closed, the circuit is not a single resistor in series

with an inductor. To answer, start by imagining what would

happen if the inductor was not there.

5.

Ã¢Ë†â€™

R2

Immediately after the switch is closed, what is the magnitude of the rate of change of current

through L? What is the direction (up/down) that the current flows through L. Justify your answer.

Hint: The inductor is in parallel with the Ã°Ââ€˜â€¦2 and must always have the same voltage.

L

5

6. A long time after the switch is closed, what is the value of the current through R2? Justify your

answer.

7. Once the circuit has reached a steady state (a long time after the switch was initially closed), the

switch is reopened. Immediately after the switch is reopened, what is the value of the current

through R2? After the switch is reopened, how much time does it take for the current in R2 to

reach approximately 37% of its initial value? Justify your answers.

Purchase answer to see full

attachment