I've tried that, and i end up with E= [(surface charge density)*(R)^2]/[2*epsilon*(R-z)^2]
where R is the hemispheres radius, and z, is a point on the z axis...
i then integrate this to find the potential between R (along the z axis), and the origin, which ends up in a divide by 0 error...
Homework Statement
I need to find the electric field along the Z-axis for a hemispherical open shell of radius R (open face down). the shell is oriented so its symmetrical about the Z axis.
The Attempt at a Solution
What I've done is set it up, taken the vector from the origin (at the...
bump. basically i need to know how to figure out work done over a non uniform 2 dimensional field. even if it requires line integrals, if someone could walk me through it
Homework Statement
F=(5y+3x-6)i + (2x-y+4)j. find work done by the force on a particle following a triangular path with verticies (0,0),(4,0),(4,3) where the positions are given in meters.
Homework Equations
Int(F(x,y))dx*dy ? not really sure for 2 dimensional problems
The Attempt...
Homework Statement
i cannot figure out how to integrate m/(am+bv) with respect to v where a, b and m are constants. i don't know if there's some simple thing I've forgotten but i can't reduce it to a constant and a simple function of v. I'm getting really frustrated as I've been working on the...
Homework Statement
i'm trying to solve the simple differential equation y'=(x+xy^2)
2. The attempt at a solution
i get dy/(1+y^2)=xdx and then integrate over the whole thing getting the solution
arctan(y)=0.5x^2+C
my problem is how do i simply this down to an equation in the form...
Homework Statement
A 17.00kg sphere is hanging from a hook by a thin wire 3.60m long, it is free to swing in a complete circle. Suddenly it is struck horizontally by a 6.00kg dart that embeds itself in the sphere. What is the minimum initial speed of the dart so the combination makes a complete...