# Chapter 2 Electric field¶

## Example 2.1 Page no 47¶

In [5]:
#Given
V=1000
d=10.0*10**-3
m=4.8*10**-15
g=10
e=1.6*10**-19

#Calculation
E=V/d
q=m*g/E
n=q/e

#Result
print"The number of electrons on the drop ", n

The number of electrons on the drop  3.0


## Example 2.2 Page no 47¶

In [21]:
#Given
e=1.6*10**-19
E=3*10**4
m=9.0*10**-31
y1=4*10**-2
m2=1.67*10**-27

#Calculation
a=e*E/m
t=math.sqrt((2*y1)/a)
a2=e*E/m2
t2=math.sqrt((2*y1)/a2)

#Result
print"Time t1=", round(t*10**9,1)*10**-9,"S","\nTime t2=",round(t2*10**7,2)*10**-7,"S"

Time t1= 3.9e-09 S
Time t2= 1.67e-07 S


## Example 2.3 Page no 48¶

In [37]:
#Given
r=1                   #m
m=9*10**9
q=500*10**-6
r1=0.3               #m

#Calculation
E=m*q/r**2
E2=m*q/r1**2

#Result
print"(i) Electric field intensity from the centre of the sphere ",E*10**-6,"10**6","N/C"
print"(ii) Electric field intensity at the surface of the sphere is ",E2*10**-7,"10**7 N/C"

(i) Electric field intensity from the centre of the sphere  4.5 10**6 N/C
(ii) Electric field intensity at the surface of the sphere is  5.0 10**7 N/C


## Example 2.4 Page no 48¶

In [33]:
#Given
q=2*10**-8
E=2*10**4
m=80*10**-6
g=9.8

#Calculation
import math
a=q*E/(m*g)
b=math.atan(a)*180/3.14
T=(q*E/(math.sin(b*3.14/180.0)))*10**-4

#Result
print"The angle is ", round(b,0),"degree"
print"Tension in the thread of the pendulum is ", round(T*10**8,2),"*10**-4 N"

The angle is  27.0 degree
Tension in the thread of the pendulum is  8.8 *10**-4 N


## Example 2.5 Page no 48¶

In [53]:
#Given
m=9*10**9
r=0.707
q=5*10**-6

#Calculation
import math
E=m*q/r**2                    #along AO
E2=m*q/r**2                   #along BO
E3=m*q/r**2                   #along OD
E11=E+E2
E12=E2+E3
I=(2*E11*r)*10**-4

#Result
print"Electric field at the centre of the sphere is ",round(I,2),"*10**4 N/C"

Electric field at the centre of the sphere is  25.46 *10**4 N/C


## Example 2.6 Page no 49¶

In [6]:
#Given
q=5*10**-9
x=0.15                  #m
r=0.1                     #m
a=9*10**9

#Calculation
E=(a*q*x)/((r**2+x**2))**1.5

#Result
print"Intensity of the electric field is ", round(E,0),"N/C"

Intensity of the electric field is  1152.0 N/C


## Example 2.7 Page no 49¶

In [10]:
#Given
m=10**-3
F=1
v0=20
v=0

#Calculation
a=-F/m
s=v**2-v0**2/(2.0*a)

#Result
print"The distance is ", s,"m"

The distance is  0.2 m


## Example 2.9 Page no 50¶

In [13]:
#Given
m=9*10**9
q1=1/3.0*10**-7
r=5*10**-2
F=58.8*10**-3

#Calculation
q2=F*r**2/(q1*m)

#Result
print"Charge is ", q2,"C"

Charge is  4.9e-07 C


## Example 2.10 Page no 61¶

In [33]:
#Given
E=4*10**5                   #V/m
q=3.2*10**-19
a=2.4*10**-10

#Calculation
import math
p=q*a
W=p*E*(1-(math.cos(180*180/3.14)))

#Result
print"Work done is ", W

Work done is  2.79670959474e-23


## Example 2.11 Page no 61¶

In [45]:
#Given
q=16*10**-19
a=3.9*10**-12
E=10**5

#Calculation
p=q*a
U=-p*E

#Result
print"(i) The electric dipole moment ", p,"Cm"
print"(ii) Potential energy of dipole in the stable equilibrium position ",U,"J"

(i) The electric dipole moment  6.24e-30 Cm
(ii) Potential energy of dipole in the stable equilibrium position  -6.24e-25 J


## Example 2.12 Page no 61¶

In [51]:
#Given
q=20*10**-6
a=10**-2
m=9*10**9
r=0.1

#Calculation
p=q*a
E=m*2*p/r**3

#Result
print"Electric field intensity is ", E*10**-5,"*10**5  N/C"

Electric field intensity is  36.0 *10**5  N/C


## Example 2.13 Page no 62¶

In [55]:
#Given
E=4*10**5
q=1*10**-6
a=3*10**-2

#Calculation
t=q*a*E

#Result
print"Maximum torque on the dipole is ", t*10**2,"*10**-2 Nm"

Maximum torque on the dipole is  1.2 *10**-2 Nm


## Example 2.14 Page no 62¶

In [60]:
#Given
q=1*10**-6
a=2*10**-2
E=10**5

#Calculation
p=q*a
W=2*p*E

#Result
print"Work done in the rotation is ", W*10**3,"*10**-3 J"

Work done in the rotation is  4.0 *10**-3 J


## Example 2.15 Page no 62¶

In [65]:
#Given
q=2*10**-6
a=0.1
m=9*10**9
r=0.5

#Calculation
p=q*a
E=m*p/r**3

#Result
print"Electric field intensity is ",E*10**-4,"*10**4 N/C"

Electric field intensity is  1.44 *10**4 N/C


## Example 2.16 Page no 62¶

In [71]:
#Given
qa=2.5*10**-7
qb=-2.5*10**-7
a=15
b=15

#Calculation
q=qa+qb
C=(a+b)*10**-2
E=qa*C

#Result
print"Total charge is ", q,"\nElectric dipole moment of the system is ",E,"Cm"

Total charge is  0.0
Electric dipole moment of the system is  7.5e-08 Cm


## Example 2.17 Page no 63¶

In [27]:
#Given
p=2*10**-8
m=9*10**9
r=1.0

#Calculation
import math
b=3*math.cos(60*3.14/180.0)**2+1
a=p*math.sqrt(b)
E=(m*a)/r**3

#Result
print"Magnitude of electric intensity is", round(E,1),"N/C"

Magnitude of electric intensity is 238.2 N/C


## Example 2.18 Page no 63¶

In [89]:
#Given
p=5*10**-8
m=9*10**9
r=0.15

#Calculation
E=m*2*p/r**3
E1=m*p/r**3

print"(i) Electric field along AB is ", round(E*10**-5,2),"*10**5 N/C"
print"(ii) Electric field along BA is ", round(E1*10**-5,2),"*10**5 N/C"

(i) Electric field along AB is  2.67 *10**5 N/C
(ii) Electric field along BA is  1.33 *10**5 N/C