# Chapter 36 INDUCTANCE¶

## Example 36.1 Inductance of a toroid¶

In [1]:
from __future__ import division
import math

u0=4*math.pi*10**-7 #in weber/amp-m   Mu-not=u0
N=10**3 #no.of turns
a=5*10**-2 #im meter
b=10*10**-2 #in meter
h=1*10**-2 #in metre
L=(u0*N**2*h)/(2*math.pi)*math.log(b/a)
print("Inductance of a toroid of recyangular cross section in henry is %.7f"%L)

Inductance of a toroid of recyangular cross section in henry is 0.0013863


## Example 36.2 Time¶

In [2]:
from __future__ import division
import math
L=50 #inductance in henry
R=30 #resistance in ohms
t0=math.log(2)*(L/R)
print("Time taken for the current to reach one-half of its final equilibrium in sec is %.7f"%t0)

Time taken for the current to reach one-half of its final equilibrium in sec is 1.1552453


## Example 36.3 Maximum Current and Energy stored¶

In [3]:
from __future__ import division
L=5 #inductance in henry
V=100 #emf in volts
R=20 #resistance in ohms
i=V/R
print("Maximum current in amp is",i)
U=(L*i**2)/2
print("Energy stored in the magnetic field in joules is %.1f"%U)

Maximum current in amp is 5.0
Energy stored in the magnetic field in joules is 62.5


## Example 36.4 Rate at which energy is stored and delivered and appeared¶

In [4]:
from __future__ import division
import math
L=3 #inductance in henry
R=10 #resistance in ohm
V=3 #emf in volts
t=0.30 #in sec
T=0.30 #inductive time constant in sec
#(a)
i=(V/R)*(1-math.exp(-t/T))
P1=V*i
print("The rate at which energy is delivred by the battery in watt is %.7f"%P1)
#(b)
P2=i**2*R
print("The rate at which energy appears as Joule heat in the resistor in watt is %.7f"%P2)
#(c)
print("Let D=di/dt")
D=(V/L)*math.exp(-t/T) #in amp/sec
P3=L*i*D
print("The desired rate at which energy is being stored in the magnetic field in watt is %.7f"%P3)

The rate at which energy is delivred by the battery in watt is 0.5689085
The rate at which energy appears as Joule heat in the resistor in watt is 0.3596188
Let D=di/dt
The desired rate at which energy is being stored in the magnetic field in watt is 0.2092897


## Example 36.6 Energy¶

In [5]:
from __future__ import division
import math

epsilon0=8.9*10**-12 #in coul2/nt-m2
E=10**5 #elelctric field in volts/meter
B=1 #magnetic field in weber/meter2
u0=4*math.pi*10**-7 #in weber/amp-m   Mu-not=u0
a=0.1 #side of the cube in meter
V0=a**3 #volume of the cube in meter3
#(a)
U1=epsilon0*E**2*V0/2 #in elelctric field
print("(a)Energy required to set up in the given cube on edge in electric field in joules is %.7f"%U1)
#(b)
U2=(B**2/(2*u0))*V0
print("(b)Energy required to set up in the given cube on edge in magnetic field in joules is %.3f"%U2)

(a)Energy required to set up in the given cube on edge in electric field in joules is 0.0000445
(b)Energy required to set up in the given cube on edge in magnetic field in joules is 397.887