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Module-1 of Model Paper-1 (Explained with solutions)
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1a] State and explain the Cylindrical coordinate systems in detail 1b] Show that electric field intensity at a point, due to ‘n’ number of point charges, is given by E⃗ = 1 4πεo ∑ Qi Ri 2 n i=1 âRi V / m. 1c] Two point charges, Q1 = 30 μC and Q2 = -100 μC, are located at (2,0,5) and (-1,0,-2)m respectively. Find (i) force on Q1(ii) force on Q2 (iii) the magnitude of forces (iv) directions of forces
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2a] State Coulomb’s law of force between any two point charges and indicate the units of the quantities involved. 2b] Show that the electric field intensity at any point due to an infinite sheet of charge is independent of the distance to the point from the sheet. 2c] Two point charges, Q1 and Q2 are located at (1, 2, 0)m and (2, 0, 0)m respectively. Find the relation between the charges, Q1 and Q2 such that the total force on a unit positive charge at (-1, 1, 0) have (i). no x-component, (ii). no y-component.
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Module-2 of Model Paper-1 (Explained with solutions)
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3a] State and prove Gauss’s law for point charge. 3b] A point charge, Q = 90 μC is located at the origin and there are surface charge distributions −8 μC /m2 at r = 1 m and 4.5 μC/m2 at r = 2 m. Find D⃗ everywhere. 3c] Calculate the divergence of D at the point specified if (i) D⃗ = (1/z2 )[10xyz âx +5×2 z ây + (2z3−5×2 y) âz] at P(−2, 3, 5) (ii) D⃗ = 5z2âr+ 10 r z âzat P(3, −450 , 5) (iii) D⃗ = 2 r sinθ sin Φ âr + r cosθ sin Φ âθ+ r cosΦ âΦ at P(3, 450 , 450 )
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4a] State & prove Divergence theorem. 4b] Obtain an expression for electric field intensity due to an infinite line charge along z- axis having a uniform charge of ρL C/m using Gauss’s law. 4c] Given D⃗ = 0.3 r2 ar nC/m2 in free space, (a) find E⃗ at P( 2, 25o , 90o ) (b) find the total charge within the sphere, r = 3. (c) Find the total electric flux leaving the sphere, r = 4, m.
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Module-3 of Model Paper-1 (Explained with solutions)
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5a] Derive expression for potential and capacitance between the planes at z=0 and z=d if the potential v = V1 and v = V2 respectively using Laplace’s equation. 5b] If potential of V = x2yz + Ay3 z Volts, i) find A so that the Laplace’s equation is satisfied. ii) With that value A, determine the electric field at a point p whose coordinates are (2, 1, -1). 5c] There exists a potential of V = -2.5 volts on a conductor at0.02 m and V = 15 volts at r = 0.35 m. Determine E and D by solving the Laplace’s equation in spherical coordinates representing the potential system.
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6a] Derivation of Ampere’s Circuital Law in point form using Strokes theorem. 6b] Derive Poisson’s and Laplace equations and writ Laplace equation in cylindrical and polar coordinates. 6c] Long concentric and right conducting cylinders in free space, at r = 5 mm and r = 25 mm in cylindrical coordinates have voltages of zero and Vo respectively. If the electric field intensity, E⃗ = -8.28×103âr at r = 15 mm, find Vo and the charge density on the outer conductor by using Laplace’s equation.
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Module-4 of Model Paper-1 (Explained with solutions)
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7a] State and Explain the force between differential Current Elements. 7b] Find the force per meter length between two long parallel wires separated by 10cm in air and carrying current of 100A in opposite direction state the nature of force between wires. 7c] Find magnetization in a magnetic material where, (i)μ = 1.8X10−5 ( H m ) and M = 120 (H m ). (ii) μr = 22, there are 8.3X1028 atoms/m3 and each atom has dipole moment of 4.5X10−27 (A.M2 ) and (iii) B=300(μT) and Xm=15.
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8a] Write short notes Magnetic Boundary Conditions. 8b] Derive the equations for Magnetic circuits with suitable diagram. 8c] A conductor 4m long lies along the y-axis with a current of 10A in the ⃗a⃗⃗⃗y direction. Find the force on the conductor if the field in the region is (in region is ) B⃗ = 0.005a⃗⃗⃗⃗x Tesla.
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Module-5 of Model Paper-1 (Explained with solutions)
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a9] What is a uniform wave? Explain its propagation in free space with necessary equations. 9b] Starting from Maxwell’s equations, derive the wave equation for sinusoidal waves in good dielectric medium. 9c] A 9.375 GHz uniform plane wave is propagating in polyethylene (εr = 2.26). If the amplitude of the electric field is 500 V/m and the material is assumed to be lossless, find ( i) Phase constant (ii) Wavelength (iii) Velocity of propagation (iv) Intrinsic impedance (v) magnetic field intensity 10a] Show that the uniform plane wave is transverse in nature. 10b] I. Write a short note on: Skin effect in conductors. II. What do you mean by depth of penetration? 10c] With respect to wave propagation in good conductors, describe what the skin effect is and derive an expression for the depth of penetration. If σ = 58 × 106 mhos/m at frequency 10 MHz, determine the depth of penetration.
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Private: ELECTROMAGNETIC THEORY || BEC401 || Model Question Paper-1 with solutions (EXPLAINED) || 2022 scheme || Video course with study materials
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