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E4. Current I flows through the wire as shown in the figure. The semicircular pant of the wire is  to x - y plane. Find the magnetic field at the centre C of the semi-circle.
Diagram
Solution: One to one of the straight pants is
B1 =  [sin900 - sin450]
Due to semi-circular pant B2 = 
Unit vector along CO = 
E5. A disc of radius R rotates at an angular velocity w about the axios perpendicular to its surface and passing through its centre. If the disc has a unifarm surface change density  , find the magnetic induction on the axis of rotation at a distance x from centre.
Solution: Consider aring of radius r and width dr.
Charge on the ring dq = (2 r dr)
Current = 
dB = 
r2 + x2 = t2 2rdr = stdt
B = 
E6. A circular loop of radius R = 20 cm is placed in a uniform magnetic field  = 2T m x - y plane. The loop carries a current i = 1.0 A in the direction shown. Find the magnetude of torque acting on the loop.
Solution: | | + = MB sin
B = 2Tp
M = NiA = 0.04
A - m2|| = 0.25
= 0.18
E7. A particle having mass m, change q and vellocity v passes through an electromagnetic field under viated. If the electric field is E0
, what we can say about the magnetic field ?
Solution: We have
B = Bx + By+ Bz
Bz= , By= 0, Bx= any value.
E8. A proton of velocity 1.0 x 107
m/s is projected at right angles to a uniform magnetic field of induction 100 wb/m2
.
How much is the particle path deflected from straight line after it has travased a distance of 1 cm in the direction of initial velocity.
np
= 1.65 x 10-27Kg , q = 1.6 x 10-19C.
Solution:
r =
SR.RE = PE.ED(0.01 m)2
= x(2r - x)
K = 4.484 x 10-5m
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