EMU PHYS102 LECTURE NOTES ALL TOPICS INCLUDED

EMU PHYS102 LECTURE NOTES

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111. PROBLEMS ABOUT ELECTRIC FLUX – 1 
A­CASE WITH UNIFORM ELECTRIC FIELD 
Prepared by Assist.Prof.Dr. I.Sakalli
P1) An electric field with a constant magnitude
 of '
4 is applied along the x‐axis. Calculate the 
electric flux through a rectangular box, which has dimensions 9H*H., as shown in the 
figure below, 
a) Calculate the electric flux through the left‐hand surface of the box, 
b) Calculate the electric flux through the right‐hand surface of the box, 
c) Calculate the electric flux through the top surface of the box, 
d) Calculate the net electric flux through the box. 
 
 
Ans: a) ?
?LFq
?tx  b) ?
Lq
?tx  c) ?
L?  d) ?
L?   
P2) Consider a closed rectangular box resting within a horizontal electric field of magnitude 
' L 7.8 H 10
8
0/%, as shown in the figure below. Calculate the electric flux through 
a) The vertical surface, 
b) The slanted (inclined) surface, 
c) The entire surface of the box, Φ
???? 
 
Ans: a) ?
LF?.??H??
?
z?
?
/o  b) ?
L?.??H??
?
z?
?
/o  c) ?
L?   
E
r
E
r

112. P3) A cone with base radius “R” and height “h” is located on a horizontal table. A horizontal 
uniform electric field ',& penetrates the cone, as shown in the figure below. Determine   
a) The electric flux that enters the left‐hand side of the cone 
b) The electric flux that leaves out from the right‐hand side of the cone 
c) The net electric flux through the cone.  
 
Ans: a) ?
?L Fq?~ b) ?
Lq?~ c) ?
L?   
 
P4) A pyramid based with a square
 having a side length sv?s?I and height 30?I is located on 
a horizontal table. A horizontal uniform electric field of magnitude '
4L20/% penetrates the 
pyramid, as shown in the figure below. Determine 
 
a) The electric flux that enters the left‐hand side of the pyramid 
b) The electric flux that leaves out from the right‐hand side of the pyramid 
c) The net electric flux through the pyramid. 
 
Ans: a) ?
?L F?. ??z?
?
/o   b) ?
L ?. ??z?
?
/o   c) ?
L?   
30cm
14.1cm
0
E
E
r

113. E
r
PROBLEMS ABOUT ELECTRIC FLUX  
B­CASE WITH NON­UNIFORM ELECTRIC FIELD and INTRODUCTION TO THE GAUSS’S LAW 
Prepared by Assist.Prof.Dr. I.Sakalli
P1) An electric field is given by ',
&L2T
6
̂ 0/%, so it is a non‐uniform electric field in the x‐
direction. A cylinder of radius “R” and height “h” has its axis aligned with the x‐axis. Its base is at 
x=0 and its top is at x=h, as shown in the figure below. Find in terms of “R” and “h”  
a) The electric flux through the base of the cylinder 
b) The electric flux through the top of the cylinder 
c) The electric flux through its cylindrical surface 
d) The total charge inside the cylinder. 
 
Ans: a) ?
L?  b) ?
L??
?

?
  
         c) ?
!L?     d) ∑?
??L?Ƚ
?
?

?
 
 
 
 
 
 
P2)
 A closed surface with dimensions a=b=60cm, c=40cm and d=50cm is located as in the 
following figure. The electric field throughout the region is nonuniform and given by                   
',
&L:3E2U
6
;̂0/%, where U is in meters. 
a) Calculate the net electric flux through the closed surface. 
b) What net charge is enclosed by the closed surface? 
 
Ans: a) ?
L?.?? ?
?
/?  b) ∑?
??L?.??H??
???
?  
y
x
z
a
b
c
E
r
d

114. P3) Four closed surfaces, S 1 through S 4, (5
7@5
8?5
6?5
5 =J@ 5
6@5
5) together with the charges 
F33, 23, 3 and F 3 are sketched in the figure below. Find the electric flux through each surface. 
 
 
Ans: a) ?
?L
???
?
?
 b) ?
?L? c) ?
?L
??
?
?
 d) ?
?L? 
P4) An infinitely long line of charge having a uniform charge per unit length ? lies a distance d 
from a point O. Determine the total electric flux through the surface of a sphere of radius R 
centered at O, when  
a)
R<d   
b) R>d 
    
Ans: a) ?
?L? b) ?
?L
?å
?
?
?
??
  
 
d
R
λ
∞−
∞

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126. 1

cm45
cm2
PROBLEMS ABOUT AMPERE’S LAW
Prepared by Prof.Dr. I.Sakalli
P1)

The end view of a very long straight wire carrying current + is shown below. Use Ampere’s law (by
drawing a suitable contour) and find the magnetic field vector at point P.

Ans: $,
&
?
LF

,
?
6?
̂





P2)
By using the result of P1,
a)
Find the total magnetic field vector at point A produced by two long straight wires with the same
currents + in opposite direction as shown in figure below.
b)
Find the magnetic force on the moving electron M
?
LF|M| , if it has a velocity R&LR
4
:̂ÊFG?; at
point A.



Ans:
a) $,
&
?
L

,
?
6?
̂
b) (&L

,
?
6?
R
4
|M|k̂EG?o

P3)

Two long thin parallel conducting wires, which are straight and perpendicularly directed to the
surface of the page carry steady currents +
5
and +
6
, as shown in the figure below. Determine the
magnetic field vector at
a)
Point #
b)
Point 2

Ans:
a) $,
&
?
LF73.2H10
?9
̂ 6
b) $,
&
?
LF:8.57̂E18.3̂;H10
?9
6




2

I
1
=10A I
2
=20A
x
z
y
KL
4cm 8cm
#1 #2
10cm
P4)

Two long thin, parallel and straight conducting wires carry steady currents +
5
and +
6
, as shown in
the figure below. Determine
a)
The magnetic field vector at point -
b)
The magnetic field vector at point .
c)
The force per unit length on the wire #2

Ans:
a) $,
&
?
L F1.33 H 10
?8
G? 6
b) $,
&
?
L3.88H10
?9
G? 6
c)
?&
?
L4H10
?8
̂ :0 I⁄;


P5)
A rectangular loop of wire is placed next to a straight wire as seen in the figure below. Both wires carry same
steady current with value 2.5#. What is the total magnetic force on the loop because of the magnetic field
created by the straight wire?

Ans: (&
???
L2.6H10
?:
̂ 0

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