Electromagnetics - 6

Medium

M1. A wire PQ of mass 10g is atvest on two parallel metallails. The separation between the rails is 4.9 cm. A magnetic field of 0.08 tesla is applied perpendicular to the plane of the rails devected downwards. The resistance of the circuit is slowly decresed. When the resistance decreases to below 20 ohm, the wire PQ begins to slide on the rails. Calculate the coeff. of friction between the wire and the rails.

Solution: µmg = ilB sin
i = E/R
µ = 0.12.

M2. Deuterons in a cyclotron describes a circle of radius 32.0 cm. Just before emerging from the D's. The frequency of the applied alternating volatge is 10 MHz.
Find
(a) Magnetic Flux Density
(b) Energy and speed of the deuterons upon emergence.
Solution: f = B = 1.30 T
v = = 2f R
             = 2.01 x 10⁷ m/s
Energy = mv² = 4.22 MeV.


M3. Calculate the force on a current carrying conductor in a uniform magnetic field as shown.



Solution: dF = I( x )
Using vector addⁿ law.
We get
F_net = I.B(a + + 2r + d)


M4. Suppose that te current density in a wire of radius a varies with r according to J = Kr² K = constant and r distance from the axis of the wire. Find the magnetic field at a point istance 1 from the axis when (i) r < a and (ii) r >a.



Solution: (i) At r distance (r < q)
dI = J dA = (Kr²)2r dr
I = K

B =

(ii) r > a
I =
B =