- #1
alexman
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Thank you for taking the time to review my work. I am posting problems with solutions, but I'm not sure if my solutions are correct. The problems are exactly how I have them written in front of me. These are mostly conceptual questions, which require a short answer of some sort.
Q1. A charge Q coulombsis placed at the origin of co-ordinates. Give the three vector force componentson a charge -Q at a point P(x,y,z).
My Answer: Fx = (k|Q||-Q|)/(r^2); Fy = (k|Q||-Q|)/(r^2); Fz = (k|Q||-Q|)/(r^2). The three vector forced components on charge -Q (at point P) would be on each of the three different axes: x,y, and z. After some calculations, you can use all three to find the direction and magnitude of charge -Q at point P.
Q2. A charge q is placed fixed at the origin. A thin hollow metal sphere radius a is centered at the origin and a charge of q is placed initially on the outside surface. After the charge has rearranged itself give the electric field
(i) at a point P(x,y,z) inside the sphere, r<a;
(ii) in the medal of the sphere, r=a;
(iii) outside the sphere, r>a.
(iv) What is the charge on the inner metal surface?
My answer:
(i) The electric field must be zero because it is that equilibrium inside the sphere. E=0
(ii) the electric field in the metal of the sphere is equal to charge q at the origin.
(iii) Outside this year, the electric field is E=(q)/(4)(pi)(Eo)(r^2). the electric field outside is uniformly spread along the surface. [got equations from book, not sure if correct].
(iv) the charge on the inner metal surface would be opposite or negative to the charge q.
Q4. Give the potential as a function of r for the three regions in problem Q2. Hint: use the fact that electric fields and potentials from different charges add. And the standard results that a sphere of radius a centered at the origin and uniformly charged with q has potential kq/a if r<a and kq/r if r>a.
My answer:
Using the hint, this is what I came up with...It's not much, but I hoping someone could help me out some more.
From Q2, using the info from the problem itself:
(i) kq/a
(ii) a=r so then kq/a = kq/r
(iii) kq/r
the different charges add, so i tried to add them
kq/a + r + kq/r
get them all the same denominator
kqr/ar + ar^2/ar + kqa/ar
so then i came up with the equation which leads me no where really
(kqr + ar^2 + kqa)/(ar) <-----this would then equal the potential as a function of r...somehow
Hopefully you have better luck with any of these problems than I did. Any input on any question would be great. Thanks for you time.
alexman
Q1. A charge Q coulombsis placed at the origin of co-ordinates. Give the three vector force componentson a charge -Q at a point P(x,y,z).
My Answer: Fx = (k|Q||-Q|)/(r^2); Fy = (k|Q||-Q|)/(r^2); Fz = (k|Q||-Q|)/(r^2). The three vector forced components on charge -Q (at point P) would be on each of the three different axes: x,y, and z. After some calculations, you can use all three to find the direction and magnitude of charge -Q at point P.
Q2. A charge q is placed fixed at the origin. A thin hollow metal sphere radius a is centered at the origin and a charge of q is placed initially on the outside surface. After the charge has rearranged itself give the electric field
(i) at a point P(x,y,z) inside the sphere, r<a;
(ii) in the medal of the sphere, r=a;
(iii) outside the sphere, r>a.
(iv) What is the charge on the inner metal surface?
My answer:
(i) The electric field must be zero because it is that equilibrium inside the sphere. E=0
(ii) the electric field in the metal of the sphere is equal to charge q at the origin.
(iii) Outside this year, the electric field is E=(q)/(4)(pi)(Eo)(r^2). the electric field outside is uniformly spread along the surface. [got equations from book, not sure if correct].
(iv) the charge on the inner metal surface would be opposite or negative to the charge q.
Q4. Give the potential as a function of r for the three regions in problem Q2. Hint: use the fact that electric fields and potentials from different charges add. And the standard results that a sphere of radius a centered at the origin and uniformly charged with q has potential kq/a if r<a and kq/r if r>a.
My answer:
Using the hint, this is what I came up with...It's not much, but I hoping someone could help me out some more.
From Q2, using the info from the problem itself:
(i) kq/a
(ii) a=r so then kq/a = kq/r
(iii) kq/r
the different charges add, so i tried to add them
kq/a + r + kq/r
get them all the same denominator
kqr/ar + ar^2/ar + kqa/ar
so then i came up with the equation which leads me no where really
(kqr + ar^2 + kqa)/(ar) <-----this would then equal the potential as a function of r...somehow
Hopefully you have better luck with any of these problems than I did. Any input on any question would be great. Thanks for you time.
alexman