ELECTROMAGNETIC FIELD THEORY-HOME ASSIGNMENT

1. Transform E field E=2cos θ ar+ sin θ aθ into Cartesian coordinates. 2. Define divergence theorem and verify both sides of this theorem for the

volume enclosed by r=2 ,z=0, and z=10,if D=(10r³/4)ar. 3. In free space, D = 2 y2 ax + 4xy ay -az mc/m2. Find the total charge stored in

the region +1≤ x ≤ 2 , 1 ≤ y ≤ 2 , -1 ≤ z ≤ 4. 4. Three point charges Q1 = 10-6 C, Q2 = -10-6 C and Q3 = 0.5 x 10-6 C are

located in air at the corners of an equilateral triangle of 50 cm side. Determine the magnitude and direction of force on Q3.

5. Show that the force on a point charge anywhere within a circular ring of uniform charge density is zero, provided the point charge remains in the plane of the ring.

6. Show that .E = 0 for the field of an uniform sheet charge in all the three coordinate systems.

7. Charge is uniformly distributed in the region -2<y<2. Use Gauss law suitably and find E at all points for which Y<-2, -2<y<2,y>2.

8. A point charge Q=30nc is located at the origin in Cartesian coordinates. Find the electric flux density D, E and potential at (1,3,-4)m.

9. A uniform line charge, ρL=25 nC/m lies on the line,x =-3, z = 4 and a uniform sheet charge ρS =50 nC/m is located at z = 4 in free space. Find E at the origin.

10. A sheet of charge ps=2nC/m2 is present at the plane x=3 in free space and line chare ρl=2nC/m is located at x=1,z=4. Find magnitude of the electric field intensity at the origin.

11. Given D=5x2ax+10zaz C/m2. Find the net outward flux crossing surface of a cube 2m on an edge centered at the origin. The edges of the cube are parallel to the axis.

12.Show that the displacement current in the dielectric of a parallel plate capacitor is equal to the conduction current in the leads.

13.Five equal point charges Q=20 nC, are placed at X=2,3,4,5 and 6. calculate potential at origin. 14.A ring of radius 10cm is charged with 10mC. Find the electric potential

and field intensity at a point 10cm away from the center of the ring, lying on a line perpendicular to the plane of the ring.

15.A line charge ρL=10 (c/m) lies along the X-axis in free space while a

point charge Q=40 C is located at (2,4,1). Three points are identified as A(1,-1,2), B(4,0,5),C(-2,-5,3) (I) find VAB (II)Find Vc if VB=0 (III) Find Vc if VA=20V.

16. Given the potential field V=5x²yz+ky³z. 1. Determine k so that Laplace’s equation is satisfied.

2. For this value of k, specify the direction of E at (2, 1,-1) by a unit Vector.

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17. A point charge 5 nC is located at the origin. If V = 2V at (0,6,-8), find the potential at A(-3, 2, 6), B(1, 5 ,7) and the potential difference VAB.

18. Given a potential V=3X²+4Y² V. Find the energy stored in the volume described by 0≤x≤1,0≤y≤1,0≤z≤1.

19. Three point charges 3, 4, 5 coulombs are situated in free space at the three corners of an equilateral triangle with side 5 cm. Find the energy density within the triangle.

20. Explain the conservative property of the electrostatic field and find the work done in moving the point charge from origin to (4,0,0) and then to (4,2,0) if E=(X/2+Y)ax+2Xay.

21. A charged particle of mass 2kg and charge 3C starts at point (1, -2, 0) with velocity 4ax+3az m/s in an electric field 12ax+10ay V/m. At time t=1s, determine the acceleration of the particle, its velocity and kinetic energy.

22. Given that H = -2 ax + 6 ay +4 az A/m in region y – x – z ≤ 0 where µ = 5µ0. Calculate magnetic flux density.

23. A conductor of length 2.5 m located at z = 0, x = 4m carries a current of 12 A in the - ay direction. Find the components of the uniform field B in the region if the force on the conductor is 1.20 x 10-2 N in the direction (−ax + a z) /√2 .

24.Two magnetic materials meet at the interface z = 0, material 1 has a relative permeability of 4 and material 2 has relative permeability of 2. The

magnetic flux density in material 1 is given by B1 = 0.1ax + 0.2ay + 0.3az tesla. Calculate the surface current density at the interface and magnetic flux density in material 2.

25. Calculate the energy stored in a magnetic field of a solenoid 50 cm long and 4 cm diameter wound on a cylindrical paper tube with 2500 turns of wire carrying current of 10 amperes.26. A current sheet K = 9 a x A/m lies in z = 10 m plane and current filament is located at y = 0, z = 8 m. Determine I in current filament if H = 0 at

P(5, 0, 2) m.27. Given µ = 3 x 10-5 H/m, = 1.2 * 10-10 F/m and σ = 0 everywhere, if

H = 2 cos (1010 t – βx) az A/m. use Maxwell’s equation to find ‘β’.28. Find α, β, γ and η for ferrite at 10GHz when Єr = 9, μr =4, σ= 10 mS/mt.29. Find the skin depth at a frequency of 2 MHz in aluminium where σ= 38.2 M S/mt. and μr =2. Also find the distance at which the amplitude of the field becomes 50% of its value at z=0.30. A uniform plane wave at a frequency of 1 GHz is travelling in a large block of dielectric (Єr =55, μr =1 and σ=0.05 S/m) . Determine γ , η, β and λ.

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