Homework Statement
In the figure the left surface of a dielectric lens is that of a circular
cylinder, and the right surface is a plane. If E1 at point P(r,45,z) in
region 1 is 5\hat{a}_{r}-3\hat{a}_{\phi }, what must be the dielectric
constant of the lens if the electric field in the...
Homework Statement
The electric potential of a grounded conducting sphere of radius r in a
uniform electric field E_{0}\hat{k}along the z direction is given by
V(r,\theta )=-E_{0}r\cos \theta +\frac{E_{0}R^{3}\cos \theta }{r^{2}}
where r is the distance from the centre of the sphere...
Sorry, i can't understand even now.
They'll be at a distance 2R apart.(i think)
and the equation of motion is,
\ddot{r}=\frac{L^{2}}{mr^{3}}-\frac{Gm}{2r^{2}}
how can i solve this?
I tried in terms of energy also.
E=\frac{1}{2}m\dot{r}^{2}+\frac{L^{2}}{2mr^{2}}-\frac{Gm^{2}}{r}...
Homework Statement
A Lagrangian for a particular physical system can be written as,
L^{\prime }=\frac{m}{2}(a\dot{x}^{2}+2b\dot{x}\dot{y}+c\dot{y}^{2})-\frac{K%
}{2}(ax^{2}+2bxy+cy^{2})
where a and b are arbitrary constants but subject to the condition that b2
-ac≠0.What are the...
Homework Statement
A particle of mass m moves in 1D such that it has Lagrangian,
L=\frac{m^{2}\dot{x}^{4}}{12}+m\dot{x}^{2}V(x)-V_{2}(x)
where V is some differentiable function of x.Find equation of motion and describe the nature of motion based on the equation.
The Attempt at a...
Homework Statement
A binary system consists of two stars of equal mass m orbiting each other in a circular orbit under the influence of gravitational forces. The period of the orbit is τ . At t = 0, the motion is stopped and the stars are allowed to fall towards each other. After what time t...
∂Homework Statement
I've some doubts in the basic quantum mechanics.I know these are too simple. But can't figure out the exact answer.
1. Ordinary wave equation relates second order time derivative to second order space derivative.But Schrodinger equation connects first order time...
Homework Statement
Consider a parallel plate air filled capacitor with plate area 10cm2
seperated by a distance 2mm.The potential difference across the plate varies
as V=360 sin(2π 106t) volts, where t is in seconds.Neglecting
the fringe effects calculate the displacement current flowing...
Homework Statement
A particle of mass m is subjected to a potential V(x)=Kx.Use uncertainty principle in the form Δx.Δp≈h(bar)/2 to estimate ground state energy of the particle.
The Attempt at a Solution
I have no idea. :(
Homework Statement
The wavefunction describing state of a system is,
\psi (r,\theta ,\phi )=\frac{1}{8\sqrt{\pi }}\left( \frac{1}{a_{0}}%
\right) ^{3/2}\frac{r}{a_{0}}e^{-4/2a_{0}}\sin \theta e^{-i\phi }
Find the parity of system in this state.
The Attempt at a Solution
\psi...
In a book i saw tha spin parity of oxygen is found by considering proton number only.I want to confirm if it is so even when the proton shell is completely filled(ie, there's no unpaired proton).or do i need to consider neutron number?