# Chapter 4 Gauss theorem¶

## Example 4.1 Page no 88¶

In [4]:
#Given
E=25                           #V/m
s=150*10**-4                    #m**2
a=60                            #degree

#Calculation
import math
A=E*s*math.cos(a*3.14/180.0)

#Result
print"Flux of the electric field is",round(A,4),"Nm**2/C"

Flux of the electric field is 0.1877 Nm**2/C


## Example 4.2 Page no 88¶

In [10]:
#Given
E=3*10**3               #N/C
S=10**-2                    #m**2

#Calculation
import math
a=E*S
A=E*S*math.cos(60*3.14/180.0)

#Result
print"(a) Flux of the field is",a,"Nm**2/C"
print"(b) Flux through the square is", round(A,0),"Nm**2/C"

(a) Flux of the field is 30.0 Nm**2/C
(b) Flux through the square is 15.0 Nm**2/C


## Example 4.3 Page no 88¶

In [14]:
#Given
e=8.854*10**-12                        #C**2/N/m**2
q=1                                    #C

#Calculation
a=q/e

#Result
print"Number of electric lines are",round(a*10**-11,3)*10**11

Number of electric lines are 1.129e+11


## Example 4.4 Page no 88¶

In [18]:
#Given
a=8*10**3                    #Nm**2/C
e=8.854*10**-12               #C**2/N/m**2

#Calculation
q=a*e

#Result
print"(a) Net charge inside the box is",q,"C"
print"(b) If the net outward flux is zero,we can't conclude that the charge inside the box is zero."

(a) Net charge inside the box is 7.0832e-08 C
(b) If the net outward flux is zero,we can't conclude that the charge inside the box is zero.


## Example 4.5 Page no 89¶

In [23]:
#Given
q=10**-5
e=8.854*10**-12

#Calculation
a=q/(6.0*e)

#Result
print"Magnitude of electric flux is", round(a*10**-5,2),"*10**5 Nm**2/C"

Magnitude of electric flux is 1.88 *10**5 Nm**2/C


## Example 4.6 Page no 89¶

In [26]:
#Given
E=9*10**4                         #N/C
r=0.04                                #m
m=9*10**9

#Calculation
l=E*r/(2.0*m)

#Result
print"Linear charge density is", l,"C/m"

Linear charge density is 2e-07 C/m


## Example 4.7 Page no 89¶

In [31]:
#Given
a=5*10**-6                       #C/m**2
e=8.854*10**-12                   #C**2/Nm**2
r=0.1                             #m
a1=60                             #Degree

#Calculation
import math
A=(a*math.pi*r**2*math.cos(a1*3.14/180.0))/(2.0*e)

#Result
print"Electric flux is", round(A*10**-3,2),"*10**3 N m**2/C"

Electric flux is 4.44 *10**3 N m**2/C


## Example 4.8 Page no 89¶

In [38]:
#Given
a=17*10**-22                       #C/m**2
e=8.854*10**-12

#Calculation
E=a/e

#Result
print"(a) Electric field to the left of the plate is zero"
print"(b) Electric field to the right of the plate is zero"
print"(c) Electric field between the plates is",round(E*10**10,2)*10**-10,"N/C"

(a) Electric field to the left of the plate is zero
(b) Electric field to the right of the plate is zero
(c) Electric field between the plates is 1.92e-10 N/C


## Example 4.9 Page no 89¶

In [51]:
#Given
q=1.6*10**-7                        #C
R=0.12                              #m
m=9*10**9
r=0.18

#Calculation
E=(m*q)/R**2
E1=(m*q)/r**2

#Result
print"(a) ELectric field inside the sphere is zero"
print"(b) Electric field outside the sphere is",E,"N/C"
print"(c) Electric field at a point 18 cm from the centre is", round(E1*10**-4,2),"*10**4 N/C"

(a) ELectric field inside the sphere is zero
(b) Electric field outside the sphere is 100000.0 N/C
(c) Electric field at a point 18 cm from the centre is 4.44 *10**4 N/C


## Example 4.11 Page no 90¶

In [56]:
#Given
e=50
V=0.2
m=9*10**9

#Calculation
q=e*V**2/m

#Result
print"Charge contained in the sphere is",round(q*10**10,2)*10**-10,"C"

Charge contained in the sphere is 2.22e-10 C