A disk of radius a has a total charge Q uniformly distributed over its surface.
A disk of radius a has a total charge Q uniformly distributed over its surface. The disk has negligible thickness and lies in the xy plane. If the electric potential is
V(z) =2kQ/a^2(√(a^2+z^2))-z what is the ELECTRIC FIELD?
Homework Answers
Consider a circular disk of radius a that is uniformly charged Q. We are interested to find the potential at a distance z from the center of the disk that is in xy plane. For convienence let us consider a disk of radius R, whose charge is dq. The distance from the edge of the disk to the point on the z axis is √[R^2+z^2].
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A disk of radius a has a total charge Q uniformly distributed over its surface.
Potential of a Charged Disk
A disk of radius \(a\) has a total charge \(Q\) uniformly distributed over its surface. The disk has negligible thickness and lies in the \(x y\) plane. Throughout this problem, you may use the variable \(k\) in place of \(\frac{1}{4 \pi \epsilon_{0}}\)Part AWhat is the electric potential \(V(z)\) on the \(z\) axisas a function of \(z,\) for \(z>0\) ? Express your answer in terms of \(Q, z\), and \(a\). You may use \(k\) instead of \(\frac{1}{4 \pi \epsilon_{0}}\).Part BWhat is...
A ring with radius R and a uniformly distributed total charge Q lies in the xy plane, centered at the origin. (Figure 1)
A ring with radius R and a uniformly distributed total charge Q lies in the xy plane, centered at the origin. (Figure 1) Part B What is the magnitude of the electric field E on the z axis as a function of z, for z >0?
(a) A conducting sphere of radius R has total charge Q, which is distributed uniformly on its surface.
1) (a) A conducting sphere of radius R has total charge Q, which is distributed uniformly on its surface. Using Gauss's law, find the electric field at a point outside the sphere at a distance r from its center, i.e. with r > R, and also at a point inside the sphere, i.e. with r < R. (b) A charged rod with length L lies along the z-axis from x= 0 to x = L and has linear charge density λ(x)...
Fully Worked solution with explanation A disk of radius R in the xz plane has total...
Fully Worked solution with
explanation
A disk of radius R in the xz plane has total charge Q
distributed non-uniformly on it
A disk of radius R in the xz plane has total charge Q distributed non-uniformly on it?s surface as described by charge density: sigma = Cr2 . 1. Find the constant C. 2. Calculate the electric field by integrating over the charge distribution. 3. Find the potential a fixed distance of y from the center of the disk....
A hollow cylinder of radius R and length l has a total charge Q uniformly distributed...
A hollow cylinder of radius R and length l has a total charge Q uniformly distributed over its surface. The axis of the cylinder coincides with the z axis, and the cylinder is centered at the origin. Obtain an expression for the electric potential as a function of z. Sketch a graph of the electric potential as a function of distance z, for -2l < z < 2l.
A sphere has a total charge Q uniformly distributed over its volume. The field inside the...
A sphere has a total charge Q uniformly distributed over its volume. The field inside the sphere at a radius r is given by Er= k (Q/R^3) r (a) What is the electric field at a radius r from the center of the sphere, where r > R (i.e outside of the sphere)? (b) Write down an expression for the electric potential at a radius r for r > R (i.e. outside of the sphere). (c) What is the electric...
A total charge of Q is uniformly distributed around the perimeter of a circle with radius a in the x-y plane centered at origin as shown in Figure P4
1. A total charge of Q is uniformly distributed around the perimeter of a circle with radius a in the x-y plane centered at origin as shown in Figure P4. (a) Find the electric field at all points on the z axis, i.e., (0,0,z). (b) Use the result you obtain in (a) to find the electric field of an infinite plane of charge with surface charge density ps located at the x-y plane. 2. Find the electric field due to a...
Problem 6 Charge Q is uniformly distributed over a circular ring on the xy plane with...
Problem 6 Charge Q is uniformly distributed over a circular ring on the xy plane with an inner and outer radius a and b, respectively. Calculate the electric field at any point on the z axis by using Coulomb's law. Then, calculate the electric potential on the z axis and use this expression to find the z component of the electric field. Check that the electric field calculated through the potential is the same as the one calculated by using...
A conductive sphere has a total charge Q uniformly distributed over its surface except at a...
A conductive sphere has a total charge Q uniformly distributed over its surface except at a point A, where there is no charge. Assuming that the point A has a 1/50 of the total area of the sphere. a) find an expression for the total electric field of the system on the axis between the center of the sphere and the center of the point A. b) calculate the electric filed at points r = 0, r = 0.9R, r...
Please explain and solve 3 Apl 2019 04) (25 points) The figure shows a non-conducting (thin) disk with a hole. The radius of the disk is Ri and the radius of the hole is R1. A total charge Q is un...
Please explain and solve
3 Apl 2019 04) (25 points) The figure shows a non-conducting (thin) disk with a hole. The radius of the disk is Ri and the radius of the hole is R1. A total charge Q is uniformly distributed on its surface electric potential at infinity is zero, what is the el distance x from its center? (20 points) b) Use electric potential to determine the electric field at point P. (S points) . Assuming that the...
Fully Worked solution with
explanation
A disk of radius R in the xz plane has total charge Q
distributed non-uniformly on it
A disk of radius R in the xz plane has total charge Q distributed non-uniformly on it?s surface as described by charge density: sigma = Cr2 . 1. Find the constant C. 2. Calculate the electric field by integrating over the charge distribution. 3. Find the potential a fixed distance of y from the center of the disk....
Problem 6 Charge Q is uniformly distributed over a circular ring on the xy plane with an inner and outer radius a and b, respectively. Calculate the electric field at any point on the z axis by using Coulomb's law. Then, calculate the electric potential on the z axis and use this expression to find the z component of the electric field. Check that the electric field calculated through the potential is the same as the one calculated by using...
Please explain and solve
3 Apl 2019 04) (25 points) The figure shows a non-conducting (thin) disk with a hole. The radius of the disk is Ri and the radius of the hole is R1. A total charge Q is uniformly distributed on its surface electric potential at infinity is zero, what is the el distance x from its center? (20 points) b) Use electric potential to determine the electric field at point P. (S points) . Assuming that the...
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