Phy223 Exam III (Form1) Professor Zuo Fall 2019

“On my honor, I have neither received nor given aid on this examination”

Signature:______________________ Name:___________________

ID number:___________________

Enter your name and Form 1 (FM1) in the scantron sheet.

Attempt all problems. All questions are worth 5pts each for a total 105 pts.

This is a closed book exam, you must work independently! No collaboration is allowed.

Prohibited items: any electronic devices including cell phones and calculators, pens, backpacks,

notes, books.

Anyone found cheating during the exam will automatically receive an “F” grade for the course

and sent to the honor’s court.

Put an X next to your discussion section:

[ ] 5P, 11:00 – 11:50 a.m.

[ ] 5Q, 12:30 – 1:20 p.m.

[ ] 5R, 2:00 – 2:50 p.m.

[ ] 5S, 3:30 – 4:20 p.m.

1) Ions having equal charges but masses of M and 2M are accelerated through the same potential

difference and then enter a uniform magnetic field perpendicular to their path. If the heavier ions

follow a circular arc of radius R, what is the radius of the arc followed by the lighter?

A) 4R, B) 3R, C) √2 R, D) R/√2 , E) R/2

2) An electron moving with a velocity = 5.0 × 107 m/s î enters a region of space where

perpendicular electric and a magnetic fields are present. The electric field is =10 kV/m ĵ. What

magnetic field will allow the electron to go through the region without being deflected?

A) = +2.0 × 10-4 T ĵ

B) = -2.0 × 10-4 T ĵ

C) = +2.0 × 10-4 T

D) = -2.0 × 10-4 T

E) = +5.0 × 10-4 T

3) A semicircular ring of radius R with a current I flowing counter-

clockwise, as shown, is inside a magnetic field �⃑� =B �̂�.

What is the magnetic force acting on the semicircular (curved) part

of the semi-loop?

A) 2RIB 𝑗̂ B) -2RIB 𝑗̂ C) 2RIB �̂� D) -2RIB �̂� E) 0

4) What is the magnetic potential energy of the semi-loop ?

A) 𝐵𝜋𝑅2𝐼 B)−𝐵𝜋𝑅2𝐼 C) 𝜋

2𝑅2𝐵𝐼 D) −

𝜋

2𝑅2𝐵𝐼 E) 0

5. Current I is flowing in the path as shown, two arcs of a circle connected by radial lengths of

wire. Find the magnetic field at point C in terms of R1, R2, Ɵ and I.

A) 𝜇𝑜𝐼𝜃

4𝜋(

1

𝑅1+

1

𝑅2) , 𝑂𝑢𝑡 𝑜𝑓 𝑝𝑎𝑔𝑒

B) 𝜇𝑜𝐼𝜃

4𝜋(

1

𝑅1−

1

𝑅2) , into the page

C) 𝜇𝑜𝐼𝜃

4𝜋(

1

𝑅1−

1

𝑅2) , 𝑜𝑢𝑡 𝑜𝑓 𝑡ℎ𝑒 𝑝𝑎𝑔𝑒

D) 𝜇𝑜𝐼𝜃

4𝜋(

1

𝑅1+

1

𝑅2) , 𝑖𝑛𝑡𝑜 𝑡ℎ𝑒 𝑝𝑎𝑔𝑒

E) None of above

For the next two questions, consider three parallel wires

each carrying a current I in the direction as shown.

6. Find the magnetic field at the site of middle wire

A) 𝜇𝑜𝐼

2𝜋𝑑 B)

𝜇𝑜𝐼

𝜋𝑑 C)

𝜇𝑜𝐼

2𝜋𝑑2 D) 𝜇𝑜𝐼

4𝜋𝑑 E) 0

7. Find the magnetic force acting on the bottom wire per unit length

A) 𝜇𝑜𝐼2

4𝜋𝑑, ↓ B)

𝜇𝑜𝐼2

4𝜋𝑑, ↑ C)

𝜇𝑜𝐼2

2𝜋𝑑, ↓ D)

𝜇𝑜𝐼2

2𝜋𝑑, ↑ E) None of above

8. Consider two positive charges q and q’ moving with v and v’ respectively, as shown. Find the

magnetic force on q due to q’?

A) 1

4𝜋𝜀0

𝑞𝑞′

4𝑑2 up

B) 𝜇𝑜

4𝜋(𝑞′𝑣′𝑞𝑣

𝑑2 ) down

C) 𝜇𝑜

4𝜋(𝑞′𝑣′𝑞𝑣

𝑑2 ) up

D) 𝜇𝑜

4𝜋(𝑞′𝑣′𝑞𝑣

4𝑑2 ) down

E) 𝜇𝑜

4𝜋(𝑞′𝑣′𝑞𝑣

4𝑑2 ) up

For the next four questions, consider a long, straight wire with a

circular cross section of radius R carries a total current 𝐼𝑜. The

current density is not uniform across the cross section, but rather

varies as J=αr, where α is a constant.

9. Find the total current 𝐼𝑜 in terms of α and R.

A) 𝐼𝑜 = 𝜋𝛼𝑅3 B) 𝐼𝑜 =𝜋𝛼𝑅3

2 C) 𝐼𝑜 =

2𝜋𝛼𝑅3

3 D) 𝐼𝑜 = 𝛼𝑟𝜋𝑅2 E) None of above

10. Using Ampere’s law to calculate the magnetic field at r=R/2.

A) 𝜇𝑜𝑎𝑅2

2 B)

𝜇𝑜𝑎𝑅2

3 C)

𝜇𝑜𝑎𝑅2

4 D)

𝜇𝑜𝑎𝑅2

12 E) None of above

11. Find the magnetic field outside of the wire at r=2R in term of 𝐼𝑜

A) 𝜇𝑜𝐼𝑜

2𝑅 B)

𝜇𝑜𝐼𝑜

4𝑅 C)

𝜇𝑜𝐼𝑜

4𝜋𝑅 D)

𝜇𝑜𝐼𝑜

4𝜋𝑅2 E) None of above

12. Find the magnetic flux going through the shaded area of width R and length W.

A) 𝜇𝑜𝑎𝑅3𝑤

3 B)

𝜇𝑜𝑎𝑅3𝑤

6 C)

𝜇𝑜𝑎𝑅3𝑤

9 D)

𝜇𝑜𝑎𝑅3𝑤

12 E) None of above

For the next 2 questions, consider a rectangular loop of wire moves with a constant speed v from

a field-free region into a region of uniform B field, as shown. In the graphs from I to V, the

vertical axis corresponds to the flux, induced

current, force required to move the loop,

respectively, instead of just i as labeled. The

horizontal axis is for time t.

13. Which of the five graphs correctly shows

the flux going through the loop as a function

of time t?

A) I

B) II

C) III

D) IV

E) V

14. Which of the five graphs correctly shows the force required to move it at constant velocity

as a function of time t?

A) I

B) II

C) III

D) IV

E) V

15. A rectangular loop of cross sectional area A is rotating about y axis at constant angular

velocity 𝜔. What is the magnetic flux going through the loop when the induced emf is zero?

A) BA or –BA

B) 0

C) BA/2

D) BA/3

E) None of above

For the next two questions, consider a long solenoid with a time-dependent current going

through it. The figure shows the cross section of the solenoid with the magnetic field going into

the page and the current i going through the coil increases with time in the form of 𝑖(𝑡) =

𝐼𝑜(1 − 𝑒−𝑡

𝜏) where t is time and 𝐼𝑜 and 𝜏 are constants. The solenoid has n turns per unit length

and radius R. For the question here, consider point a at r=R/2.

16. Find the magnitude of magnetic field at point a at 𝑡 = 0

A) 0

B) 𝜇𝑜𝑛𝐼0

C) 𝜇𝑜𝑛𝐼0/𝑒

D) 𝜇𝑜𝐼0/2𝑅

E) None of above

17. Find the induced electric field at point a at 𝑡 = 𝜏

A) 0 B) 𝜇𝑜𝑛𝐼0𝑅

8𝜏𝑒𝑖̂ C)

𝜇𝑜𝑛𝐼0𝑅

4𝜏𝑒𝑗 ̂ D)

𝜇𝑜𝑛𝐼0𝑅

4𝜏𝑒𝑖̂ E)−

𝜇𝑜𝑛𝐼0𝑅

4𝜏𝑒𝑖̂

18. Find the electric field on the x-axis at x=2R at t = 𝜏

A) 0 B) 𝜇𝑜𝑛𝐼0𝑅

4𝑒𝜏𝑗̂ C) −

𝜇𝑜𝑛𝐼0𝑅

4𝑒𝜏𝑗̂ D)

𝜇𝑜𝑛𝐼0𝑅

4𝑒𝜏𝑖̂ E) −

𝜇𝑜𝑛𝐼0𝑅

4𝑒𝜏𝑖̂

For the next three questions, consider a rod is being

pulled to the left at constant speed v on conducting rails.

A constant current i flows in the long wire in the

direction indicated. The rod, rails, and connecting strip

at the right form a conducting loop. The rod has

resistance R; the rest of the loop has negligible

resistance.

19. Calculate the total magnetic flux going through the

loop when the moving rod is a distance x from the

conducting strip.

A) 𝜇𝑜𝑖𝑥𝐿

2𝜋𝑎 B)

𝜇𝑜𝑖𝑥𝐿

2𝜋(𝑎+𝐿) C)

𝜇𝑜𝑖𝑥

2𝜋𝑙𝑛(

𝐿+𝑎

𝑎)

D) 𝜇𝑜𝑖𝑥

4𝜋𝑙𝑛(

𝐿+𝑎

𝑎) E) None of above

20. Find the magnitude and direction of the induced current in the loop.

A) 𝜇𝑜𝑖𝑣

2𝜋𝑅𝑙𝑛 (

𝐿+𝑎

𝑎) , 𝑐𝑤 B)

𝜇𝑜𝑖𝑣

2𝜋𝑅𝑙𝑛 (

𝐿+𝑎

𝑎) , 𝑐𝑐𝑤 C)

𝐵𝐿𝑣

𝑅, 𝑐𝑤 D)

𝐵𝐿𝑣

𝑅, 𝑐𝑐𝑤 E) None of above

21. Find the magnitude of the force necessary to keep it moving at the constant velocity in terms

of induced current Iin.

A) 𝐼𝑖𝑛𝑅

𝑣 B)

𝐼𝑖𝑛2𝑅

𝑣 C)

𝐼𝑖𝑛2𝑣

𝑅 D)

𝐼𝑖𝑛2𝑣2

𝑅 E) None of above

x