Bissoy.com
Doctors Medicines MCQs Q&A

If $${\text{W}} = \phi + {\text{i}}\psi $$   represents the complex potential for an electric field. Given $$\psi = {{\text{x}}^2} - {{\text{y}}^2} + \frac{{\text{x}}}{{{{\text{x}}^2} + {{\text{y}}^2}}},$$     then the function $$\phi $$ is

If $${\text{W}} = \phi + {\text{i}}\psi $$   represents the complex potential for an electric field. Given $$\psi = {{\text{x}}^2} - {{\text{y}}^2} + \frac{{\text{x}}}{{{{\text{x}}^2} + {{\text{y}}^2}}},$$     then the function $$\phi $$ is Correct Answer $$ - 2{\text{xy}} + \frac{{\text{y}}}{{{{\text{x}}^2} + {{\text{y}}^2}}} + {\text{C}}$$

Related Questions

A particle of mass m is confined in the potential
Quantum Mechanics mcq question image
\[V\left( x \right) = \left\{ {\begin{array}{*{20}{c}} {\frac{1}{2}m{\omega ^2}{x^2},}&{{\text{for }}x Let the wave function of the particle be given by $$\psi \left( x \right) = - \frac{1}{{\sqrt 5 }}{\psi _0} + \frac{2}{{\sqrt 5 }}{\psi _1}$$
where $${\psi _0}$$ and $${\psi _1}$$ are the eigen functions of the ground state and the first excited slate respectively. The expectation value of the energy is
Potential function $$\phi $$ is given as $$\phi $$ = x2 - y2. What will be the stream function $$\psi $$ with the condition $$\psi $$ = 0 at x = y = 0?
If the electrostatic potential were Igiven by $$\phi = {\phi _0}$$  (x2 + y2 + z2), where $${\phi _0}$$ is constant, then the charge density giving rise to the above potential would be
S = Training data = => No (negative example). How will S be represented after encountering this training data?
The value of $$\left( {\frac{{\sin \theta + \sin \phi }}{{\cos \theta + \cos \phi }} + \frac{{\cos \theta - \cos \phi }}{{\sin\theta - \sin\phi }}} \right)$$       is?
Consider the line integral $$I = \int_{\text{c}} {\left( {{{\text{x}}^2} + {\text{i}}{{\text{y}}^2}} \right){\text{dz,}}} $$    where z = x + iy. The line c is shown in the figure below
Complex Variable mcq question image
The value of $$I$$ is
The cumulative distribution function for the lognormal distribution is given by _____ \) b) \(\phi\) c) \(\phi\) d) \(\phi\)
Consider the following remarks pertaining to the irrotational flow: 1. The Laplace equation of stream function \(\frac{{{\delta ^2}{\rm{\Psi }}}}{{\delta {x^2}}} + \frac{{{\delta ^2}{\rm{\Psi }}}}{{\delta {y^2}}} = 0\) must be satisfied for the flow to be potential. 2. The Laplace equation for the velocity potential \(\frac{{{\delta ^2}{\rm{\varphi }}}}{{\delta {x^2}}} + \frac{{{\delta ^2}{\rm{\varphi }}}}{{\delta {y^2}}} = 0\) must be satisfied to fulfil the orate . of mass conservation i.e continuity equation.. Which of the above statements is/are correct?
If $${\text{sin}}\left( {{{60}^ \circ } - \theta } \right)$$   = $${\text{cos}}\left( {\psi - {{30}^ \circ }} \right),$$   then the value of $${\text{tan}}\left( {\psi - \theta } \right)$$   is (assume that $$\theta $$ and $$\psi $$ are both positive acute angles with$$\theta {30^ \circ }$$  ) ?
A particle is in the normalized state $$\left| \psi \right\rangle $$ which is a superposition of the energy eigen states $$\left| {{E_0} = 10\,eV} \right\rangle $$   and $$\left| {{E_1} = 30\,eV} \right\rangle .$$   The average value of energy of the particle in the state $$\left| \psi \right\rangle $$ is 20 eV. The state $$\left| \psi \right\rangle $$ is given by