Question

the electrostatic force vector F for a system of unit charges is defined by vector F=(x^2+y^2+z^2)^n...

the electrostatic force vector F for a system of unit charges is defined by vector F=(x^2+y^2+z^2)^n (xi+yj+zk). where is an integer. Find (a) div vector F, (b) a scalar potential psi such that F =-delta psi. Leave your answer in terms of vector |r| where vector r=(xi+yj+zk).

the electrostatic force vector F for a system of unit charges is defined by vector F=(x^2+y^2+z^2)^n (xi+yj+zk). where is n an integer. Find (a) div vector F, (b) a scalar potential psi such that F =-delta psi. Leave your answer in terms of vector |r| where vector r=(xi+yj+zk).

Science   Advanced-Physics   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

(a) I have calculated the divergence in cartesian co-ordinates and then converted to spherical co-ordinates.

(b) This is also very straightforward question.

I have equated x-components in last part. You can also do this by equating y- and z- components.The answer would be same.

Hope you find it useful. Sorry for any calculation mistake. have a nice day :)

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Find the flux of F across S, S F · N dS where N is the...
Find the flux of F across S, S F · N dS where N is the upward unit normal vector to S. F(x, y, z) = xi + yj + zk S: z = 1 − x^2 − y^2, z ≥ 0
] Evaluate the surface integral SF∙dS for the vector field Fx,y,z=xi+yj+zk , where S is the...
] Evaluate the surface integral SF∙dS for the vector field Fx,y,z=xi+yj+zk , where S is the surface given by z=1-x2-y2, z≥0 , where S has the positive (outward) orientation. Note: SF∙N dS=RF∙-gxx,yi-gyx,yj+kdA
A) Consider the vector field F(x,y,z)=(9yz,−8xz,8xy). Find the divergence and curl of F. div(F)=∇⋅F= ? curl(F)=∇×F=(...
A) Consider the vector field F(x,y,z)=(9yz,−8xz,8xy). Find the divergence and curl of F. div(F)=∇⋅F= ? curl(F)=∇×F=( ? , ? , ?) B) Consider the vector field F(x,y,z)=(−4x2,0,3(x+y+z)2). Find the divergence and curl of F. div(F)=∇⋅F= ? curl(F)=∇×F=( ? , ? , ?).
1. A function f : Z → Z is defined by f(n) = 3n − 9....
1. A function f : Z → Z is defined by f(n) = 3n − 9. (a) Determine f(C), where C is the set of odd integers. (b) Determine f^−1 (D), where D = {6k : k ∈ Z}. 2. Two functions f : Z → Z and g : Z → Z are defined by f(n) = 2n^ 2+1 and g(n) = 1 − 2n. Find a formula for the function f ◦ g. 3. A function f :...
Evaluate the line integral ∫CF⋅dr, where F(x,y,z)=5xi+yj−2zk and C is given by the vector function r(t)=〈sint,cost,t〉,...
Evaluate the line integral ∫CF⋅dr, where F(x,y,z)=5xi+yj−2zk and C is given by the vector function r(t)=〈sint,cost,t〉, 0≤t≤3π/2.
(1 point) Evaluate the line integral ∫CF⋅dr∫CF⋅dr, where F(x,y,z)=3xi+4yj-zk and C is given by the vector...
(1 point) Evaluate the line integral ∫CF⋅dr∫CF⋅dr, where F(x,y,z)=3xi+4yj-zk and C is given by the vector function r(t)=〈sint,cost,t〉, 0≤t≤3π/2.
Calculate differentiability of f(x,y,z) = x^2 + y^2 + z^2 this function is defined in R^2
Calculate differentiability of f(x,y,z) = x^2 + y^2 + z^2 this function is defined in R^2
Let f(x, y) =sqrt(1−xy) and consider the surface S defined by z=f(x, y). find a vector...
Let f(x, y) =sqrt(1−xy) and consider the surface S defined by z=f(x, y). find a vector normal to S at (1,-3)
17 Find curl F A) F=z^2xi+y^2zj-z^2yk B) given vector field F= (x+xz^2)I +xyj +yzk, Find div...
17 Find curl F A) F=z^2xi+y^2zj-z^2yk B) given vector field F= (x+xz^2)I +xyj +yzk, Find div and curl of F.
] Consider the function f : R 2 → R defined by f(x, y) = x...
] Consider the function f : R 2 → R defined by f(x, y) = x ln(x + 2y). (a) Find the gradient of f(x, y) at the point P(e/3, e/3). (b) Use the gradient to find the directional derivative of f at P(e/3, e/3) in the direction of the vector ~u = h−4, 3i. (c) Find a unit vector (based at P) pointing in the direction in which f increases most rapidly at P.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT