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 potential inside the sphere?
A sphere has a total charge Q uniformly distributed over its volume. The field inside the...
Charge Q is uniformly distributed inside a sphere of radius R. (a) Determine the electric field inside and outside the sphere. Explain how you arrive at the answer. (b) A cavity of radius R/4, and centered at a point a distance R/2 from the center of the sphere, is made within the sphere. This means that within the sphere of radius R, there is a smaller sphere of radius R/4 which has no charge (the charge density is zero within...
Charge Q = +4.00 μC is distributed uniformly over the volume of an insulating sphere that has radius R = 5.00 cm. What is the potential difference between the center of the sphere, V(0) and the surface of the sphere, V(R)? Solve by finding the E-field inside the insulating sphere using Gauss law, and then find the potential difference.
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...
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)...
Charge Q=+ 2.00 μC is distributed uniformly over the volume of an insulating sphere that has radius R = 3.00 cm . Part A What is the potential difference between the center of the sphere and the surface of the sphere?
Charge Q = 2E-6 C is distributed uniformly over the volume of an insulating sphere that has radius R = 3cm What is the potential difference between the center of the sphere and the surface of the sphere if the sphere is metallic and we place the same charge Q on it?
A nonconducting sphere of radius r0 carries a total charge Q distributed uniformly throughout its volume. Part A: Determine the electric potential as a function of the distance r from the center of the sphere for r>r0. Take V=0 at r=?. Part B: Determine the electric potential as a function of the distance r from the center of the sphere for r<r0. Take V=0 at r=?. Express your answer in terms of some or all of the variables r0, Q,...
An isolated thin spherical conducting shell of radius R has charge Q uniformly distributed on its surface. Write the results in terms of k, Q and R. (a) Find the electric field at a distance, r = 2R from the center of the sphere. (b) What is the electric field at the center of the conducting sphere? What is the electric field inside the conducting sphere? Please explain the steps and formuals. Mandatory !!!
A non-uniformly charged sphere of radius R has a total charge Q. The electric field inside this charge distribution is described by E=Emax(r4 /R4 ), where Emax is a known constant. Using the differential form of Gauss’s law, find volume charge density as a function of r. Express your result in terms of r, R and Emax.
Consider a sphere of radius a with a uniform charge distribution over its volume, and a total charge of q_o. Use Gauss's Law to calculate the electric field outside the sphere, and then inside the sphere. Solve the general problem in r, recognizing that problem spherical symmetry. Draw a graph of the electric field the has the surface of the strength as a function of noting where if the surface of the sphere is (a). Some hints: the surface area...