Overlapping Charged spheres: solve Electric Force of point charge (Q) locations

[staple123]

I need help understanding how to calculate various Electric Field Strengths of several point charges (Q) both inside and along two OVERLAPPING identical spheres BUT with on NON-UNIFORM VOLUME CHARGE DENSITIES (-1p non-overlap density on the outside with -4p density overlapping internally) with both having identical radii (R). These spheres are identical expect for these volume charge densities.

I started with: E(sphere) = Q/4pi(Eo)R^2

1) Is E(total) as the sum of three vectors: E1, E2, E(overlap) and combine all three to calculate the net total (Etot)? OR: Is it just the two overlapping identical spheres minus (-) the overlapping common segment?

2) Is this the best formula for this scenario: Volume Density (ro: P) = Q/V(subscript little r)I=Q/(4/3)(pi)(r^2)?

Are there any "special" integration issues that must be evaluated first for that common overlapped segment that the two spheres share in common when solving for E(sphere)?

3) What are the trignomentric X, Y components of an abritary point charge Q that is placed along the edge of where these two overlapping spheres intersect with identical radius (r) at angle theta? The point Q is in between the two overlapping spheres at the 12 O-clock position in the respective X,Y plane Cartesian plane.

specifically, what is the easiest way to calculate strength of the Electric Field (E) at this common tangental point charge Q and its X,Y trigonmetric components (X hat, Y hat).

* assume 1st quadrant rules of TRIG are applied at this location for point charge: Q.

thank you for any advice...:-)

 

[anathema]

Hello, I can definitely help you understand how to calculate the Electric Field Strengths of point charges inside and along two overlapping identical spheres with non-uniform volume charge densities. Let's break down the questions one by one.

1) To calculate the total Electric Field (Etot) at any point, you will need to add the individual Electric Fields (E1 and E2) from each sphere and the Electric Field (Eoverlap) from the overlapping region. The net total Electric Field can be calculated using the vector addition formula: Etot = E1 + E2 + Eoverlap. This will give you the total Electric Field at the point in question.

2) The formula you have mentioned for calculating the volume charge density (ro) is correct. However, it is important to note that the volume charge density in the overlapping region will be different from the non-overlapping region. You will need to calculate the volume charge density separately for each region and then use the appropriate formula to calculate the Electric Field.

3) To calculate the Electric Field at a point charge Q placed along the edge of where the two spheres intersect, you will need to use the Electric Field formula for a point charge: E = kQ/r^2, where k is the Coulomb's constant, Q is the charge of the point charge, and r is the distance from the point charge to the point where you want to calculate the Electric Field. To find the X and Y components of the Electric Field, you can use trigonometric functions such as sine and cosine. For example, the X component of the Electric Field can be calculated as Ex = E*cos(theta), where theta is the angle between the X axis and the line connecting the point charge and the point where you want to calculate the Electric Field.

I hope this helps you understand how to calculate the Electric Field Strengths in this scenario. If you have any further questions, please don't hesitate to ask. Good luck!