# Physics 203 Sample Exam 1

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18 Οκτ 2013 (πριν από 4 χρόνια και 6 μήνες)

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Physics 203
Sample

Exam 1

Gothard Grey

Spring 2008

Name _________________

a b c d

[1] = =

=

[2]

= = =

[3] =

= =

[4] = =

=

[5]

= = =

[6]

= = =

[7] = = =

[8] = =

=

[9] =

= =

[10] = = =

Mass of proton = 1.67E
-
27 kg

Mass of alpha = 4 x mass of proton

Charge of alpha = +4e

+ my 3 x 5 card which is on line.
Multiple choice, 3 points each

[1] An electron a proton and an
alpha particle enter a uniform magnetic field, all moving
at the same velocity. The particle with the largest radius for its trajectory is the

(a) electron.

(b) proton.

(c) alpha particle.

(d) all the same.

[2] For the particles in question 1, which

particle curves in the opposite direction from
the other two upon entering the field?

(a) electron.

(b) proton.

(c) alpha particle.

(d) all the same.

[3] As you move away from a long, straight wire carrying an electric current, the strength
of the mag
netic field varies as

(a) 1/r
2

(b) 1/r

(c) ln(r)

(d) r

[4] A magnetic field exerts a force on all the following
EXCEPT

(a) a current carrying wire

(b) a moving electric charge

(c) a stationary electric charge

(d) a magnet

[5] Which of the followin
g will not drive an electric current in a conductive loop?

(a) magnetic flux through the loop

(b)
a potential difference along the loop

(c) an electric field around the loop

(d) a changing magnetic flux through the loop

[6] The presence of a ferr
omagnetic core in the center of a coil

(a) concentrates the magnetic field.

(b) spreads the magnetic field lines out.

(c) only serves to support the coil.

(d) is necessary to produce a magnetic field.

[7] A light wave

(a) constant el
ectric and magnetic fields.

(b) oscillating electric and magnetic fields in the same direction.

(c) electric and magnetic fields at various angles.

(d) oscillating electric and magnetic fields at right angles.

[8]
Magnetic fields can be pr
oduced by

(a) electric currents

(b) changing electric flux

(c) both a and b

(d) none of these

[9]
The circuit in the diagram at right will allow
what signals to pass?

(a) low frequencies

(b) high frequencies

(c) DC signals

(
d) no signals.

[10]

The energy stored in an electric field is proportional to

(a) 1/E
2

(b)1/E

(c) E

(d)E
2

Choose one of problems A or B to do. Show all work. If you have extra time, you
may work on the other for extra credit.

5 points per part.

[A] Two solenoids are next to each other, oriented end to end along the same axis.
Solenoid A is 20 cm long, 4 cm. in diameter and has 200 turns.

Solenoid B has 5 turns per cm., is 15 cm long and 5 cm. in diameter.

(a) Calculate the inductance of sole
noid B.

L = NBA/I = N
2

o

R
2
/l = (5x15)
2

(4

E
-
7 T

m/A)

(2.5E
-
2)
2

m
2
/0.15m

= 9.25E
-
5
T

m
2
/A

(b) Given a current of 4sin(10t) in solenoid A, calculate the flux in solenoid B. You may
assume no leakage of field from between the solenoids .

Flux in B =
B

A

for coil B = (

o
n
A
I)(

r
A
2
) since B field confined to area of
coil A (or spreads out to give same flux in coil B.

Flux = (4

E
-
7 T

m/A)(1000 turns/m)(4sin(10t) A)

(.02m)
2

=
6.32E
-
6

Tm
2

(c) Calculate the induced voltage in solenoid B

given a magnetic fiel
d of 4sin(20t)
everywhere inside it
.

V =
-
d/dt (BA) =
-
d/dt[(4sin(20t) A)

(.025m)
2
]

=
-

80

(.025m)
2

cos(20t)

=
-
0.157

cos(20t) Tm
2
/s =
-
0.157

cos(20t)V

(d)
For a current of 2 Amps in solenoid A, calculate the magnetic field inside solenoid A.

B =

o
n
A
I = 4

E
-
7 T

m/A)(1000 turns/m)(2A) =
2.51E
-
3 T

(e) A proton from a cosmic ray enters the field on a path perpendicular to the axis of the
solenoid. Calculate the radius of the path of the proton in the field.

p = Ber; r = mv/Be = (
1.67E
-
27 kg )v
/[(2.51
E
-
3 T)(1.6E
-
19 C)]

Oops!, use v = 2.4 E5 m/s

r= (1.67)(2.4)/[(2.51)(1.6)] kg m/(s T C)

= 1.00 m
[B] Electrons are held in a circular path of 2 km. and are moving at a velocity of

3.0E6 m/s. A total of 10E10 electrons are in the beam.

(a) This b
eam has what current?

Current = A = C/s, Here, this is given by

Nqv/2
πr = (1.6E
-
19 C)(10E10)(3.0E6 m/s)/(2π 2E3 m) = 3.8E
-
7 A

(b) What magnetic field does this beam produce at the center of the 2km ring?

B field at center of a ring with current I: B = μ
o
I/2R

B = (4πE
-
7 T

m/A)(3.8E
-
7 A)/(4E3 m) = 1.19E
-
16 T

(c) What is t
he cyclotron frequency for the electrons in this beam?

2π v/

r =

=
V/r

= (3.0E6 m/s)/(2E3m) =
1.50

(
d
) To keep the electron beam in its circular path, what magnetic field must be used and
what direction does it point if the beam circulates
clockwise?

Clockwise beam of electrons = CCW current. Right hand rule for IxB=F with
F toward center of circle gives B downward.

Now use p=Ber, B = mv/(er) = (9.11E
-
31 kg)(3.0E
-
6 m/s)/[(1.6E
-
19 C)(2E3 m)]

= 8.54E
-
21 kg/Cs = 8.54E
-
21 T

(
e
) If a magne
tic field of 0.2 Tesla is produced with a solenoid carrying a current of 5
Amps,
what can you say about the construction of the solenoid (number of coils, length,
area,..)?

For a solenoid, B=
μ
o

n I where n = turns/m.

So we have 0.2T = (4πE
-
7 T m/A) n (5 A)

Gathering numbers to the left,

3.18E4 /m = n = turns per meter.
Do one of questions C and D, 20 points.

[C] A square loop, a cm x b cm, lies on a table with 2 wires. One wire carries 2 a
mps, is
parallel to the side of length b and is y cm away from the closest side. The second wire
carries 5 amps, is parallel to the side of length a and is x cm away.

(a) Draw a diagram.

(b) Derive the expression for the magnetic field produced by eac
h current.

B =

o
I/(2

r) so, for top, B
1

=

o
2/(2

r
1
) =

o
/(

r
1
) into page

for side, B
2

=

o
5/(2

r
2
) out of page.

(c) Derive the total magnetic flux in the loop using superposition.

For top wire, B
1

the same for horizontal strips in rectangle,

so,
B

=

o
/(

r
1
),
dA

= bdr
1

and limits are r
1

= y to y+a

1

=

y

y+a

o
/(

r
1
) bdr
1

=

o
b/

y

y+a

dr
1

/ r
1

= (

o
b/

) ln([y+a]/a) into page

For side wire, B
2

the same for vertical strips in rectangle,

so,
B

= 5

o
/(2

r
2
),
dA

2

and limits ar
e r
2

= x to x+b

2

=

x

x+b

5

o
/(2

r
2
2

= 5

o
a/2

x

x+b

dr
2

/ r
2

= (
5

o
a/2

) ln([x+b]/b) out of page

Superposition:

Add, but in opposite direction. Call out of page positive,

=

2

-

1

=
(
5

o
a/2

) ln([x+b]/b)
-

(

o
b/

) ln([y+a]/
a) out of page.
[D] A long solenoid with n turns per meter carries current I in the wire. The solenoid has

(a) Use Ampere’s Law to find the magnetic field inside the solenoid.

∫B

ds = μ
o

I enclosed

B is zero outside the solenoid and
perpendic
ular to the integration path
for the vertical legs.

Inside the solenoid, B and ds are
parallel, giving ∫B

ds = B L = μ
o

I

where L = length of leg inside solenoid. For I, there are N turns inside the
integration path, each carrying current I, so we have

BL = μ
o

NI B = μ
o

NI/L = μ
o

nI n = N/L

(b) Determine the magnetic flux inside the solenoid.

Since the above result is independent of where in the solenoid the lower leg
of the loop is, B is uniform and perpendicular to the cross section (parallel t
o
dA) so we have

= ∫B

dA = B∫dA = BA = μ
o

nIπR
2

(c) A particle with mass m and charge q enters the field along a path making an angle of
45

with the axis of the solenoid. Find an expression for its trajectory. You can split the
trajectory into two mo
tions to make it simpler.

Split the velocity into components parallel to and perpendicular to the
magnetic field direction. (In this case, both = v/√2). Call the direction of the
B field z.

The parallel component remains unchanged, so z = v/√2 t.

For the

other component, p=Ber applies; here,

mv/√2 = Bqr

r = mv/(√2 Bq) gives the radius of the path and

2πR /(v/√2 ) gives the period = 2π√2 R/v