Chapter 8 Magnetic field due to electric current

Example 8.1 Page no 417

In [36]:
#Given
q=1.6*10**-19                  #c
B=0.1                          #T
v=5.0*10**6                      #m/s
a=90                           #degree

#Calculation
import math
Fm=q*v*B*math.sin(a)

#Result
print"Force on the proton is", round(Fm*10**14,1)*10**-14,"N"

Force on the proton is 7.2e-14 N

Example 8.2 Page no 417

In [34]:
#Given
n=1.0*10**29                          #m**-3
e=1.6*10**-19                           #C
A=2*10**-6                                       #m**2
I=5                                       #A
B=0.15                                   #T
a=90                                     #degree

#Calculation
import math
Vd=I/(n*e*A)
Fm=e*Vd*B*math.sin(a)

#Result
print"Force acting on each electron is", round(Fm*10**24,2)*10**-24,"N"

Force acting on each electron is 3.35e-24 N

Example 8.3 Page no 417

In [44]:
#Given
q=2*1.6*10**-19                  #C
v=6*10**5                        #m/s
B=0.2                             #T
a=90                              #degree
m=6.65*10**-27

#Calculation
import math
Fm=q*v*B*math.sin(a)
a=Fm/m

#Result
print"Force on alpha particle is", round(Fm*10**14,2)*10**-14,"N"
print"Acceleration of alpha particle is",round(a*10**-12,2)*10**12,"m/s**2"

Force on alpha particle is 3.43e-14 N
Acceleration of alpha particle is 5.16e+12 m/s**2

Example 8.4 Page no 426

In [64]:
#Given
a=60                         #degree
u=4*3.14*10**-7                 #T/A m
Bc=2

#Calculation
import math
a=(Bc/2.0)/(math.tan(60)*180/3.14)
B1=(10**-7*math.tan(60)*(math.sin(60*180/3.14)+math.sin(60*180/3.14)))*10
B=3*B1

#Result
print"Magnetic fieldat the centroid of the triangle is", round(B*10**7,0),"*10**-7 T"

Magnetic fieldat the centroid of the triangle is 10.0 *10**-7 T

Example 8.5 Page no 426

In [68]:
#Given
n=20
I=1                  #A
r=0.08                  #m
u=4*3.14*10**-7             #T/A m

#Calculation
B=u*n*I/(2*r)

#Result
print"Magnitude of the magnetic field is", B*10**4,"*10*4 T"

Magnitude of the magnetic field is 1.57 *10*4 T

Example 8.6 Page no 426

In [71]:
#Given
u=10**-7
I=10*10**-2                       #A
r=0.5

#Calculation
B=u*I/r**2

#Result
print"Magnetic field on Y axis is", B,"K^ T"

Magnetic field on Y axis is 4e-08 K^ T

Example 8.7 Page no 426

In [82]:
#Given
I=5               #A
l=0.01              #m
a=45              #degree
r=2               #m
u=10**-7

#Calculation
import math
B=(u*I*l*math.sin(a)*180/3.14)/r**2

#Result
print"Magnetic field is", round(B*10**8,1)*10**-10,"T"

Magnetic field is 6.1e-10 T

Example 8.8 Page no 427

In [87]:
#Given
u=4*3.14*10**-7                     #T/A m
n=20
I=12                                  #A
r=0.1                                 #m

#Calculation
B=u*n*I/(2*r)

#Result
print"Magnetic field at the centre of coil is", round(B*10**3,1),"*10**-3 T"

Magnetic field at the centre of coil is 1.5 *10**-3 T

Example 8.12 Page no 429

In [92]:
#Given
r=0.02             #m

#Calculation
B=u*I/(4*r)

#Result
print"The magnitude of magnetic field is", round(B*10**4,2),"*10**-4 T"

The magnitude of magnetic field is 1.88 *10**-4 T

Example 8.13 Page no 429

In [98]:
#Given
v=4*10**6
r=0.5*10**-10
e=1.6*10**-19
t=1

#Calculation
import math
f=v/(2.0*math.pi*r)
I=f*e/t
B=u*I/(2*r)

#Result
print"Magnetic field produced by the electrons is", round(B,1),"T"

Magnetic field produced by the electrons is 25.6 T

Example 8.15 Page no 430

In [109]:
#Given
n=100
I=5                          #A
r=0.1                        #m
x=0.05

#Calculation
B=u*n*I/(2*r)
B1=(u*n*I*r**2)/(2.0*(r**2+x**2)**1.5)

#Result
print"(i) Magnetic field at the centre of the coil is",B*10**3,"*10**-3 T"
print"(ii) The magnetic field at the point on the axis of the coil is",round(B1*10**3,2),"*10**-3 T"

(i) Magnetic field at the centre of the coil is 3.14 *10**-3 T
(ii) The magnetic field at the point on the axis of the coil is 2.25 *10**-3 T

Example 8.18 Page no 431

In [118]:
#Given
a=5*10**-2
I=50
e=1.6*10**-19
B1=10**7

#Calculation
import math
B=u*I/(2*math.pi*a)
F=e*B1*B

#Result
print"(i) Force on electron when velocity is towards the wire", round(F*10**16,1)*10**-16,"N"
print"(ii) Force on electron when velocity is parallel to the wire", round(F*10**16,1)*10**-16,"N"
print"(iii) Force on electron when velocity is perpendicular to the wire is zero"

(i) Force on electron when velocity is towards the wire 3.2e-16 N
(ii) Force on electron when velocity is parallel to the wire 3.2e-16 N
(iii) Force on electron when velocity is perpendicular to the wire is zero

Example 8.20 Page no 432

In [127]:
#Given
e=1.6*10**-19
f=6.8*10**15
r=0.51*10**-10

#Calculation
import math
I=e*f
B=(u*I)/(2*r)
M=1*I*math.pi*r**2

#Result
print"The effective dipole moment is",round(M*10**24,0)*10**-24,"Am**2"

The effective dipole moment is 9e-24 Am**2

Example 8.22 Page no 439

In [3]:
#Given
n=5*850/1.23
I=5.57                    #A

#calculation
u=4*math.pi*10**-7
B=u*n*I

#Result
print"Magnitude of magnetic field is", round(B*10**3,1),"*10**-3 T"

Magnitude of magnetic field is 24.2 *10**-3 T

Example 8.23 Page no 439

In [138]:
#Given
r1=20
r2=25
I=2                   #a

#Calculation
import math
r=(r1+r2)/2.0
l=(2*math.pi*r)*10**-2
n=1500/l
B=u*n*I

#Result
print"(i) Magnetic field inside the toroid is", round(B,3),"T"
print"(ii) magnetic field outside the toroid is zero"

(i) Magnetic field inside the toroid is 0.003 T
(ii) magnetic field outside the toroid is zero

Example 8.25 Page no 440

In [142]:
#Given
I=2                         #A
R=5*10**-2                          #m
r=3*10**-2                            #m

#Calculation
import math
B=u*I*r/(2*math.pi*R**2)

#Result
print round(B*10**6,1),"*10**-6 T"

4.8 *10**-6 T