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PG Notes 2011 : Physics (Banaras Hindu University (BHU), Varanasi )

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Brijmohan
Banaras Hindu University (BHU), Varanasi
PhD Condensed matter Physics
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fiziks Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES ELECTROMAGNETIC THEORY JRF/NET (JUNE-2011) Q1. The electrostatic potential V(x, y) in free space in a region where the charge density is zero is given by V x, y 4e 2 x f x 3 y 2 . Given that the x-component of the electric field Ex, and V are zero at the origin, f(x) is (a) 3x 2 4e 2 x 8x (c) 4e 2 x 8 Ans: (b) 3x 2 4e 2 x 16 x (d) 3x 2 4e 2 x (d) Solution: V 4e 2 x f x 3 y 2 . Since 0 2V 0 16 e 2 x f x 6 0 . Since E x 0 at origin E V Ex 8e 2 x f x E x 0, 0 8 f 0 0 f 0 8 . Since V 0, 0 0 4 f 0 0 f 0 4 Solve equation 16 e 2 x f x 6 0 f x 6 16 e 2 x f x 6 x 8e 2 x c1 , since f 0 8 c1 0 . Again Integrate f x 6 x 8e 2 x f x 3x 2 4e 2 x c 2 since f 0 4 c2 0 . Thus f x 3x 2 4e 2 x Q2. For constant uniform electric and magnetic field E E0 and B B0 , it is possible to choose a gauge such that the scalar potential and vector potential A are given by 1 (a) 0 and A B0 r 2 (c) E0 r and A 0 Ans: 1 (b) E0 r and A B0 r 2 (d) 0 and A E0 t (a) y z y z and B B0 x since they are constant vector. Solution: Let E E0 x V Lorentz Gauge condition is A 0 0 t Head office fiziks, H.No. 23, G.F, Jia Sarai, Near IIT, Hauz Khas, New Delhi-16 Phone: 011-26865455/+91-9871145498 Website: www.physicsbyfiziks.com Email: fiziks.physics@gmail.com Branch office Anand Institute of Mathematics, 28-B/6, Jia Sarai, Near IIT Hauz Khas, New Delhi-16 1

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