phy102 exam i spring 2012-key(1)

7/31/2019 PHY102 Exam I Spring 2012-Key(1)

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1. A positive point charge of magnitude 2.5 C is at the center of an uncharged conductingspherical shell of inner radius a= 60 cm and outer radius b=90 cm.

a- find the charge densities on the inner and outer surfaces of the shell and the total

charges on the surfaces?

b- Find the electric field everywhere ( r


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Ev

Solution:

(a) Since E is vertical, the electric force is vertical, and the resulting acceleration has only a y-

component (ax = 0)

-7

5

0.051.11 10 111

4.50 10 /x

x mt s ns

v m s= = = =

(b)

( ) ( )

( )

19 3

11 2

27

1.6 10 9.60 10 /

9.21 10 m s1.67 10y

C N CqE

a m kg

= = =

21

2f i yi yy y v t a t = + :

( ) ( )2

11 7 31 9.21 10 1.11 10 5.68 10 m 5.68 mm2

fy = = =

(c) 54.50 10 m sx

v =

( ) ( )11 7 59.21 10 1.11 10 1.02 10 m syf yi yv v a t = + = =

3. A hollow non-conducting spherical shell of inner radius R1 and outer radius R2 carries a

total charge of Q distributed uniformly throughout its volume. Determine the electric

flux through a spherical surface of radius r (R1 < r < R2 ) concentric with the shell.

Solution:

According to G. L.

E= oencq /

Then we have to calculate encq within the surface of radius

r (R1 < r < R2 ).

As the charge is uniformly distributed, thenencq = V`, where V` is the volume of the shell within G.S. that has a charge;

encq = V` =)(3/4

3

1

3

2 RRQ

( )(3/4

3

1

3 Rr

r

R2

R1


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Therefore

E=oenc

q

/ = )( 3132 RR

Q

o )(

3

1

3

Rr


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4. A charged cork ball of mass 2g is suspended from a light string in the presence of a

uniform electric field. When the field E = (3i+ 4j) 105N/C, the ball is in equilibrium at

= 30o. Find the charge on the ball.

The equilibrium conditions are

0 =xF

0 =yF

T cos30 + qEy mg = 0

Tsin30 qEx =0

T cos30 + q (4 105) 2 10-3(9.8)= 0 1

and

Tsin30 q (3 104)=0 2

From 2 w get T = 15000q substitute in 1

q = 4.1 X 10-8 C

q

g = 9.8m/s2

E

phy102 exam i spring 2012-key(1)

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