Electromagnetics - 5

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 C_O =


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 = (2r 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 = 2T
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 = B_x + B_y + B_z

B_z = ,  B_y = 0,   B_x = 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.
n_p = 1.65 x 10^-27 Kg ,    q = 1.6 x 10^-19C.

Solution:



r =
SR.RE = PE.ED
(0.01 m)² = x(2r - x)
K = 4.484 x 10^-5 m