JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech II ELECTROMAGNETIC FIELDS Previous Question Paper (October - 2020 - R16)
Answer any five questions. All questions carry equal marks.
Main
Find the electric field intensity due to infinite line charge.
Answer
Consider an infinitely long straight line charge with a uniform charge density ρL (C/m) placed along the z-axis. To find the electric field intensity E at a radial distance r from the line, we apply Gauss's Law: ∮ D · dS = Qenc.
We choose a cylindrical Gaussian surface of radius r and length L. The surface consists of three parts: the top disk, the bottom disk, and the curved side surface. Due to symmetry, the electric field is purely radial (E = Er ar). The flux through the top and bottom disks is zero because the electric field vector is perpendicular to the surface normal vector (dS is in the az direction). Thus, the total flux is limited to the side surface.
Solving for Dr:
Since D = εE, the electric field intensity is:
Derive Poisson’s and Laplace equations starting from point form of Gauss Law.
Answer
Starting from the point form of Gauss's Law, the divergence of the electric flux density D is equal to the volume charge density ρv:
Using the constitutive relation D = εE and the gradient relationship E = -∇V, we substitute these into the Gauss Law equation:
Assuming a homogeneous medium where ε is constant, we obtain Poisson's equation:
In a charge-free region where ρv = 0, the equation simplifies to Laplace's equation:
State and prove Gauss’s law as applied to an electric field and determine the field due to an infinite line charge.
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Define the potential difference and absolute potential. Give the relation between potential and field intensity.
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Derive boundary conditions between two perfect dielectrics.
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Obtain the ohm’s law in point form.
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Derive the expression for energy stored and energy density in a static electric field.
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Derive an expression for the capacitance of a parallel plate capacitor having two dielectric mediums.
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State and prove Biot-savart’s law and also derive the Maxwell’s second equation from it.
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Derive the expression for force between two current carrying conductors.
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Explain the Ampere’s law and its significance with respect to Maxwell’s equation for magnetostatics.
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Derive the expression for torque on a current loop placed in magnetic field.
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Derive the expression for inductance of a toroidal coil carrying current I, with N turns and the radius of toroid is R.
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Explain statically induced e.m.f and dynamically induced e.m.f?
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Explain modified ampere’s law for time varying fields.
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