The charged sphere A spherical shell has spherical symmetry and because of this we write its potential as $V(R,\theta)=V_0(\theta)$ ($\theta$ is the “polar” angle of the spherical coordinate system). a)… Click here to read more
Electron wave An electron travels toward negative values of $x$ having a kinetic energy $E=2 eV$. Please write the equation of this electron wave and describe its characteristic values. The… Click here to read more
What is the potential of the infinite slot from Griffiths 3.3, if you are given a varying potential $V(0,y)=V_0x/a$ as a boundary condition at $x=0$ For the given arrangement of… Click here to read more
You are given two charges $q_0$ and $q$ situated on the z axis at $z=+a$ and $z=-a$. What are the monopole and dipole terms in the potential, when the distance… Click here to read more
For a square loop of side $a$ in a magnetic field $mathbf{B}=B_0[1-(x^2/l^2)]*hat x$ rotating with angular velocity $omega$ please find $E(t)$ induced in loop. In text it says that the… Click here to read more
Find the reflection coefficient of a plane wave with energy $E>V$ on a “step potential” initially 0 that drops down to $-V_0$. How is this similar and different to a… Click here to read more
For a uniform current that goes through a long cylinder (z-axis) please find a) force exerted by the upper half on the lower half of the cylinder. b) magnitude of this… Click here to read more
This is an explanation of why rotation along the long axis of molecule is forbidden by quantum mechanics.a) What is the definition of moment of inertia $I$ for rotational motion?b)… Click here to read more
What is the magnetic field at a distance $z$ from the center of an equilateral triangle of side $a$, that has a current $I$. Verify that it reduces to the… Click here to read more
A hollow cube has conducting walls defined by 6 planes $x=y=z=0$ and $x=y=z=a$. The walls at $z=0$ and $z=a$ are held at a constant potentail $V_0$. The other four sides… Click here to read more
Determine the potential on the z-axis of a nonuniform charged circle that has a linear charge densitya) $lambda =C*sin phi$b) $lambda =C*sin 2phi$c)$lambda =C*sin 3phi$d) $lambda =Cphi$ $d q=λ*d L=λR*dϕ$ … Click here to read more
You are given a wire along the $z$ axis, of radius $a$. For the magnetic field $B=B0(frac {y+a}{a})hat x$, the current density is $J=J0(frac{a-s}{a})hat z$.a. Determine the current in the… Click here to read more
There is a surface charge density $rho_{s0}$on the surface of a cylinder $rho=a$, $0 < z < L$, $0 < phi < 2pi$. What is the electric field $overrightarrow{E}$ at… Click here to read more
Given that $D = (r^2cos(phi/2)$, $rsin(phi/2), 0)$ in cylindrical coordinates represents an electric flux density, calculate the total charge inside the closed surface defined by $r = 1$, $z =… Click here to read more
What is the magnetic field of the following current configurations:a) $B= (μ_0 I)/4π ∮ (dL ×r ̂)/r^2$$B= (μ_0 I)/4π {∫_1^2…+∫_0^θ(a*dθ)/a^2+∫_3^4…+∫_θ^0(b*dθ)/b^2 }$$B=(μ_0 I)/4π (0+1/a θ+0-1/b θ)$$B=(μ_0 I)/4π θ(1/a-1/b)$On 1->2 and 3->4… Click here to read more
You are given a circle in the (x y) plane that has a homogeneously distributed charge:a) What is the potential $V$ on the $z$ axis?b) What is the electric field… Click here to read more
Given the two coaxial solenoids in the image with the inside solenoid (of radius $a$ and $n1$ turns)having a current $I$ and the outside solenoid (of radius $b$ and turns… Click here to read more
What is the energy (per unit length) that is stored in an infinitely long cylinder with charge density (constant) $rho$? Consider the cylinder above (black) with a cylindrical Gaussian surface… Click here to read more
Solve for the electrostatic potential, $V (x, y)$, in the region $x \geq 0$, $0 \leq y \leq a$, defined by boundary conditions$V(x, 0) = 0$$V(x, a) = 0$$V(0, y)… Click here to read more
Consider a loop with 50 square turns that is 12 cm on a side and is in a uniform 0.6 T magnetic field. Find the current through a loop needed… Click here to read more
