UNIT-4:Electrostatics

Example no:4.1,Page no:103

In [32]:
#Variable declaration  
q=1.0          #no of coulomb
e=1.6*10**-19    #charge on an electron

#Calculation
n=(q/e)   #calculating no of electrons

#Result
print"No of electrons =",n
print"NOTE:Calculation mistake in book"

No of electrons = 6.25e+18
NOTE:Calculation mistake in book

Example no:4.2,Page no:103

In [36]:
import math  

#Variable declaration
g=9.8
m=4.5       #Massin [kg]
r=0.03      #radius in [m]

#Calculation
F=m*g    #in Newton
q=math.sqrt(((r**2)*m*g)/(9*10**9))   #calculating q using F=(1/4*3.14*eo)*((q1*q2)/(r**2))

#Result
print"Charge = ",q,"C"
print"\nNOTE:Calculation mistake in book"

Charge =  2.1e-06 C

NOTE:Calculation mistake in book

Example no:4.3,Page no:103

In [70]:
#Variable declaration  
q1=2*10**-7     #charge in C
q2=3*10**-7     #charge in C
r=30*10**-2     #r in m

#Calculation
F=(9*10**9)*((q1*q2)/r**2)   #calculating F

#Result
print"Force  = %.e"%F,"N"

Force  = 6e-03 N

Example no:4.4,Page no:104

In [71]:
#Variable declaration  
q1=1     #charge in C
q2=1     #charge in C
r=1     #r in m

#Calculation
F=(9*10**9)*((q1*q2)/r**2)   #calculating F

#Result
print"Force = %.e"%F,"N"

Force = 9e+09 N

Example no:4.5,Page no:104

In [50]:
#Variable declaration  
m=9*10**-31       #mass of electron in kg
q=-3.2*10**-7     #charge in C
e=-1.6*10**-19     #charge on electron in C

#Calculation
n=(q/e)   #calculating n
M=n*m     #calculating mass transfered

#Result
print"(a):No. of electrons = ",n
print"(b):Mass transfered to polythene= ",M,"kg"

(a):No. of electrons =  2e+12
(b):Mass transfered to polythene=  1.8e-18 kg

Example no:4.6,Page no:105

In [54]:
#Variable declaration  
q1=1.6*10**-19     #charge in C
q2=-1.6*10**-19     #charge in C
r=10**-9     #r in m

#Calculation
F=(9*10**9)*((q1*q2)/r**2)   #calculating F

#Result
print"Force=",F,"N"

Force= -2.304e-10 N

Example no:4.7,Page no:110

In [55]:
#Variable declaration  
Va=-10  #voltage in volts
W=100   #work in Joule
q=2     #charge in Coulomb

#Calculation
v=(Va)+(W/q)   #calculating v

#Result
print"Voltage = ",v,"V"

Voltage =  40 V

Example no:4.8,Page no:111

In [73]:
import math  

#Variable declaration
eo=(8.854*10**-12)    #constant
E=2    #magnitude of electric field in N/C
r=0.5   #r in m

#Calculation
q=E*4*(math.pi)*(eo)*(r**2)    #calculating charge

#Result
print"Charge= %.2e"%q,"C"
print"\nNOTE:Calcualtion mistake in book"

Charge= 5.56e-11 C

NOTE:Calcualtion mistake in book

Example no:4.9,Page no:111

In [69]:
#Variable declaration  
e=-1.6*10**-19   #charge on electron in Coulomb
q=20*10**-6   #charge in Coulomb
r1=0.1   #r1 in m
r2=0.05   #r2 in m

#Calculation
Va=9*10**9*(q/r1)   #calculating voltage at A
Vb=9*10**9*(q/r2)   #calculating voltage at B
V=Va-Vb     #potential difference
W=V*e      #calculating work done in joule

#Result
print"Work done to take the electron from A to B = ",W,"Joule"

Work done to take the electron from A to B =  2.88e-13 Joule

Example no:4.10,Page no:112

In [4]:
#Variable declaration  
q1=(2.0*10**-8)   #charge in coulomb
q2=(-2.0*10**-8)   #charge in coulomb
q3=(3.0*10**-8)   #charge in coulomb
q4=(6.0*10**-8)   #charge in coulomb
s=1.0   #side in m

#Calculation
V=(9.0*10**9)*(1.0/s)*(q1+q2+q3+q4)   #calculating voltage

#Result
print"Voltage in Volts = ",V,"Volts"
print"\nNOTE:Calculation mistake in book"

Voltage in Volts =  810.0 Volts

NOTE:Calculation mistake in book

Example no:4.11,Page no:123

In [6]:
#Variable declaration  
eo=8.85*10**-12   #constant
q=2*10**-6    #charge in coulomb
l=9    #length in cm

#Calculation
fi=(q/eo)   #calcualting flux in (N m square)/c

#Result
print"Flux through the surface=%2e"%fi,"N m^2/c"

Flux through the surface=2.259887e+05 N m^2/c

Example no:4.12,Page no:124

In [12]:
import math  

#Variable declaration
eo=8.85*10**-12   #constant
r=1.2    #r in m
t=80*10**-6   #surface sharge density in c/m square

#Calculation
q=t*4*(math.pi)*(r**2)   #calculating charge
fi=q/eo      #calculating flux

#Result
print"Flux=%g"%fi,"N c^-1 m^2"

Flux=1.63576e+08 N c^-1 m^2

Example no:4.13,Page no:124

In [3]:
import math  

#Variable declaration
eo=8.85*10**-12   #constant
E=9*10**4    #Electric field in N/C
r=2*10**-2    #r in m

#Calculation
L=2*(math.pi)*E*eo*r   #calculating linear charge density

#Result
print"Linear charge density = ",round(L,7),"cm^-1"

Linear charge density =  1e-07 cm^-1

Example no:4.14,Page no:125

In [7]:
#Variable declaration  
o=17*10**-22    #surface charge density in cm**-2
eo=8.85*10**-12   #constant

#Calculation
E=o/eo   #calculating electric intensity in region III

#Result
print"Electric Intensity in regions I and II = 0"    
print"Electric Intensity in region III  = ",round(E,12),"N/C"

Electric Intensity in regions I and II = 0
Electric Intensity in region III  =  1.92e-10 N/C

Example no:4.15,Page no:125

In [65]:
import math 

#Variable declaration
r=0.05   # in m
eo=8.85*10**-12   #constant
q=10.0**-9   #charge at point P in Coulomb

#Calculation
E=q/(4*(math.pi)*eo*(r**2))   #calculating electric field
r1=0.2   #in m
V1=q/(4*(math.pi)*eo*r1)   #calculating potential difference

#Result
print"Electric field= ",round(E),"v/m"
print"\nNOTE:Approximate answer is calculated in book\n\n"
print"Potential difference between two points = ",round(V1),"V"

Electric field=  3597.0 v/m

NOTE:Approximate answer is calculated in book


Potential difference between two points =  45.0 V

Example no:4.16,Page no:126

In [19]:
import math  

#Variable declaration
eo=8.85*10**-12   #constant
o=80.0*10**-6   #surface charge density in c/ square
r=1.2   #in m

#Calculation
q=o*(math.pi)*(r**2)   #calculating charge in Coulomb
fi=q/eo   #calculating electric flux

#Result
print"Charge= ",q,"C"
print"Electric flux  = ",fi,"N m^2/c"
print"\nNOTE:Wrong answers in book\n"

Charge=  0.000361911473694 C
Electric flux  =  40893951.8298 N m^2/c

NOTE:Wrong answers in book

Example no:4.17,Page no:138

In [68]:
#Variable declaration  
V=250   #potential difference in Volt
C=10**-11   #capacitance in farad

#Calculation
q=C*V   #calculating charge

#Result
print"Charge  = ",q,"C"

Charge  =  2.5e-09 C

Example no:4.18,Page no:138

In [67]:
#Variable declaration  
r=6.4*10**6   #in m

#Calculation
C=r/(9*10**9)   #calculating charge

#Result
print"Capacitance = ",round(C*10**6),"mu F"

Capacitance =  711.0 mu F

Example no:4.19,Page no:138

In [66]:
#Variable declaration  
C=2   #capacitance in Farad
d=0.5*10**-2   #distance in m
eo=8.85*10**-12   #constant

#Calculation
A=(C*d)/(eo)   #calculating area

#Result
print"Area=%.2e"%A,"m^2"

Area=1.13e+09 m^2

Example no:4.20,Page no:139

In [4]:
import math  

#Variable declaration
A=0.02   #area in m square
r=0.5   #r in m

#Calculation
d=(A/(4*(math.pi)*r))   #calculating distance

#Result
print"Distance between the plates = ",round(d*1000,2),"mm"

Distance between the plates =  3.18 mm

Example no:4.21,Page no:139

In [21]:
#Variable declaration  
eo=8.85*10**-12   #constant
A=1   #area in m square
d=2*10**-3   #r in m
K=4   #constant

#Calculation
C=(K*eo*A)/d    #calculating capacitance

#Result
print"Capacitance = ",C,"Farad"

Capacitance =  1.77e-08 Farad

Example no:4.22,Page no:140

In [37]:
#Variable declaration  
cm=10*10**-6   #capacitance in Farad
K=2   #constant

#Calculation
co=cm/K   #calculating co

#Result
print"capacity of capacitor with air between the plates= ",co*10**6,"muF"

capacity of capacitor with air between the plates=  5.0 muF

Example no:4.23,Page no:140

In [48]:
#Variable declaration  
v=100.0        #v in volt
c1=8.0*10**-6   #capacitance in Farad
c2=12.0*10.0**-6   #capacitance in Farad
c3=24.0*10.0**-6   #capacitance in Farad
cs=4.0/(10.0**6)   #calculating series capacitance

#Calculation
cp=(c1+c2+c3)   #calculating parallel capacitance
qs=cs*v   #calculating charge

#Result
print"Equivalent Series capacitance,C= ",cs*10**6,"muF"
print"Equivalent parallel capacitance,Cp= ",cp*10**6,"muF"    
print"charge on plate=%.e"%qs,"C"

Equivalent Series capacitance,C=  4.0 muF
Equivalent parallel capacitance,Cp=  44.0 muF
charge on plate=4e-04 C

Example no:4.24,Page no:141

In [50]:
#Variable declaration  
C=9*10**-10   #capacitance in farad
V=100.0   #in volt

#Calculation
U=(1/2.0)*(C*(V**2))   #calculating energy stored

#Result
print"Energy stored  = ",U,"J"

Energy stored  =  4.5e-06 J

Example no:4.25,Page no:141

In [56]:
#Variable declaration  
eo=8.85*10**-12   #constant
A=90.0*10**-4   #area in m square
d=2.5*10**-3    #distance in m
V=400.0   #in volt

#Calculation
C=(eo*A)/d   #calculating capacitance
W=(1/2.0)*(C*(V**2))   #calculating electrical energy stored

#Result
print"Capacitance = ",C,"Farad"
print"Electrical Energy stored in capacitor =%.2e"%W,"J"

Capacitance =  3.186e-11 Farad
Electrical Energy stored in capacitor =2.55e-06 J

Example no:4.26,Page no:142

In [60]:
#Variable declaration  
v=100        #v in volt
c1=1*10**-6   #capacitance in Farad
c2=2*10**-6   #capacitance in Farad
c3=3*10**-6   #capacitance in Farad
cs=6/11.0   #calculating series capacitance

#Calculation
cp=(c1+c2+c3)   #calculating parallel capacitance

#Result
print"Equivalent Series capacitance = ",cs,"muF"
print"Equivalent parallel capacitance= ",cp*10**6,"muF"
print"Therefore Cp=(11*Cs)"    

Equivalent Series capacitance =  0.545454545455 muF
Equivalent parallel capacitance=  6.0 muF
Therefore Cp=(11*Cs)

Example no:4.27,Page no:143

In [63]:
#Variable declaration  
eo=8.85*10**-12   #constant
V=6   #v in volt
A=25*10**-4   #area in m square
d=10**-3   #distance in m

#Calculation
q=(eo*A*V)/d   #calculating charge
W=q*V    #calculating work done

#Result
print"Charge through battery  =%.3g"%q,"C"
print"Work done by Battery=%.e"%W,"J"

Charge through battery  =1.33e-10 C
Work done by Battery=8e-10 J