5: Magnetostatics

Example number 5.1, Page number 118

In [12]:
#importing modules
import math
from __future__ import division

#Variable declaration
m=1.7*10**-27;     #mass of proton(kg)
q=1.6*10**-19;   #charge of proton(C)
KE=6*10**6*q;   #kinetic energy of proton(J) 
B=2;   #intensity of magnetic field(Wb/m**2)
theta=90*math.pi/180;   #angle(radian)

#Calculation
v=math.sqrt(2*KE/m);    #velocity(m/s)
Fb=q*v*B*math.sin(theta);   #force acting on proton(N)

#Result
print "force acting on proton is",round(Fb*10**11,3),"*10**-11 N"
print "answer given in the book is wrong"

force acting on proton is 1.075 *10**-11 N
answer given in the book is wrong

Example number 5.2, Page number 119

In [13]:
#importing modules
import math
from __future__ import division

#Variable declaration
r=6.4*10**6;    #radius of earth(m)
P=6.4*10**21;    #magnetic moment(Amp m**2)

#Calculation
A=math.pi*(r**2);    #area(m**2)
i=P/A;    #current(amp)

#Result
print "current is",round(i/10**7),"*10**7 Amp"

current is 5.0 *10**7 Amp

Example number 5.3, Page number 119

In [14]:
#importing modules
import math
from __future__ import division

#Variable declaration
B0=1.7*10**-5;    #magnetic flux density(Wb/m**2)
mew0=4*math.pi*10**-7;   

#Calculation
H=B0/mew0;    #magnetic intensity(Amp/m)

#Result
print "magnetic intensity is",round(H,1),"Amp/m"

magnetic intensity is 13.5 Amp/m

Example number 5.4, Page number 119

In [20]:
#importing modules
import math
from __future__ import division

#Variable declaration
l=30*10**-2;   #length(m)
A=10**-4;    #area(m**2)
N=300;    #number of turns
i=0.032;   #current(ampere)
phi=2*10**-6;   #magnetic flux(Wb)
mew0=4*math.pi*10**-7;   

#Calculation
B=phi/A;    #magnetic flux density(wb/m**2)
H=N*i/l;    #magnetising force(amp turns/m)
mew=B/H;    #permeability of ion(Wb/Amp m)
mewr=mew/mew0;   #relative permeability

#Result
print "magnetic flux density is",B*10**2,"*10**-2 wb/m**2"
print "magnetising force is",H,"amp turns/m"
print "permeability of ion is",mew*10**4,"*10**-4 Wb/Amp m"
print "relative permeability is",round(mewr)
print "answer for relative permeability differs due to round off errors"

magnetic flux density is 2.0 *10**-2 wb/m**2
magnetising force is 32.0 amp turns/m
permeability of ion is 6.25 *10**-4 Wb/Amp m
relative permeability is 497.0
answer for relative permeability differs due to round off errors

Example number 5.5, Page number 120

In [23]:
#importing modules
import math
from __future__ import division

#Variable declaration
M=600;   #magnetic moment(cgs units)
V=20;    #volume(cm**3)
H=50;    #magnetic field(oersteds)

#Calculation
I=M/V;   #intensity of magnetisation(cgs units)
B=H+(4*math.pi*I);   #flux density(guass)

#Result
print "flux density is",round(B),"guass"
print "answer given in the book is wrong"

flux density is 427.0 guass
answer given in the book is wrong

Example number 5.6, Page number 120

In [24]:
#importing modules
import math
from __future__ import division

#Variable declaration
m=12000;   #mass(gm)
d=7.5;   #density(g/cm**3)
new=50;   #frequency(Hz)
a=3000;   #area of hysterisis curve(erg/cm**3)

#Calculation
V=m/d;   #volume of core(cm**3)
El=a*V;  #energy loss in 1 cycle(erg)
n=new*60*60;   #number of cycles per hour
EL=El*n/10**7;   #energy loss per hour(J)

#Result
print "energy loss per hour is",EL/10**4,"*10**4 J"

energy loss per hour is 8.64 *10**4 J

Example number 5.7, Page number 121

In [25]:
#importing modules
import math
from __future__ import division

#Variable declaration
B=8*math.pi;    #magnetic flux density(wb/m**2)
H=2000;   #magnetic field(amp turn/m)
mew0=4*math.pi*10**-7;   

#Calculation
mewr=B/(mew0*H);     #relative permeability
chi=mewr-1;    #susceptibility

#Result
print "susceptibility is",chi

susceptibility is 9999.0

Example number 5.8, Page number 121

In [29]:
#importing modules
import math
from __future__ import division

#Variable declaration
q=1.6*10**-19;     #charge on electron(C)
i1=3;
j1=2;
k1=3;    #components of vector
i2=3;
j2=4;   
k2=0;    #components of vector
i3=0;
j3=4;
k3=1;    #components of vector

#Calculation
i4=(j2*k3)-(j3*k2);
j4=(i2*k3)-(i3*k2);
k4=(i2*j3)-(i3*j2);    #components of derived vector
i5=i1+i4;
j5=j1+j4;
k5=k1+k4;
F=q*math.sqrt((i5**2)+(j5**2)+(k5**2));    #Lorentz force(N)

#Result
print "Lorentz force is",round(F*10**19,2),"*10**-19 N"
print "answer given in the book is wrong"

Lorentz force is 27.67 *10**-19 N
answer given in the book is wrong