Question

2. A small charge $q$ is located at $x = (0, 0, a)$ inside a hollow grounded spherical conductor of radius $R > a$. As a result, the electrostatic potential inside the sphere becomes $\Phi(x, y, z) = \frac{q}{4\pi\epsilon_0} \left[ \frac{1}{\sqrt{x^2 + y^2 + (z - a)^2}} - \frac{1}{\sqrt{(\frac{ax}{R})^2 + (\frac{ay}{R})^2 + (R - \frac{az}{R})^2}} \right]$ 3.1. Express this potential in spherical polar coordinates. 3.2. Calculate the electric field inside the sphere.

          2. A small charge $q$ is located at $x = (0, 0, a)$ inside a hollow grounded spherical conductor of radius $R > a$. As a result, the electrostatic potential inside the sphere becomes

$\Phi(x, y, z) = \frac{q}{4\pi\epsilon_0} \left[ \frac{1}{\sqrt{x^2 + y^2 + (z - a)^2}} - \frac{1}{\sqrt{(\frac{ax}{R})^2 + (\frac{ay}{R})^2 + (R - \frac{az}{R})^2}} \right]$

3.1. Express this potential in spherical polar coordinates.
3.2. Calculate the electric field inside the sphere.

2. A small charge q is located at x = (0, 0, a) inside a hollow grounded spherical conductor of radius R > a. As a result, the electrostatic potential inside the sphere becomes

Φ(x, y, z) = (q)/(4πϵ0)[ (1)/(√(x^2 + y^2 + (z - a)^2)) - (1)/(√(((ax)/(R))^2 + ((ay)/(R))^2 + (R - (az)/(R))^2))]

3.1. Express this potential in spherical polar coordinates.
3.2. Calculate the electric field inside the sphere.

Added by Ashley C.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Khoobchandra Agrawal

07/28/2022

Step 1

In spherical polar coordinates, x = r sinθ cosφ, y = r sinθ sinφ, and z = r cosθ. Substitute these into the given potential Φ(x,y,z): Φ(r, θ, φ) = (q)/(4πε₀) * ((1)/√(r^(2) + (z-a)^(2)) - (1)/√((ar/R)^(2) + (R-z)^(2))) Show more…

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A small charge q is located at x=(0,0,a) inside a hollow grounded spherical conductor of radius R>a. As a result, the electrostatic potential inside the sphere becomes Φ(x,y,z)=(q)/(4πε₀)((1)/(sqrt(x^(2)+y^(2)+(z-a)^(2)))-(1)/(sqrt(((ax)/(R))^(2)+((ay)/(R))^(2)+(R-(az)/(R))^(2)))) 3.1. Express this potential in spherical polar coordinates. 3.2. Calculate the electric field inside the sphere. A small charge q is located at x=(0,0,a) inside a hollow grounded spherical conductor of radius R>. As a result, the electrostatic potential inside the sphere becomes Φ(x,y,z) = 47E /x2+y+(z-a 3.1. Express this potential in spherical polar coordinates 3.2. Calculate the electric field inside the sphere.