Suppose the electric field in some region is found to be E = kr^3 r, in spherica

Question

Suppose the electric field in some region is found to be E = kr^3 r, in spherical coordinates(k is constant). Find its charge density rho. In two different ways, find the total charge contained in a sphere or radius R, centered at the origin. Assume the electric field is given by E = kr^3 r Using the differential form of Gauss Law, find the charge density at x m a electric field in the region is defined as: E = {ax^2 _(N/C) for 0 lessthanorequalto x lessthanorequalto 3m bi_(N/C) for x > 3m If a charge q sits at the back corner of a cube of side s. Calculate is the flux of E through the right shaded side of the cube as shown? Assume q = 1C.

Explanation / Answer

a) From Gauss's law ,del.E = / 0

del . E =1/r2 / r ( r2 k r3) =1/r2 k(5 r4) = 5kr2

=  0 (del .E ) = 5kr2 0

b) by Gauss's law , E.ds =Q/0

Q =0 E.ds

the electric field at the surface of the sphere is obtained by considering a gaussian surface of radius R.

then the electric field at the surface of the sphere is E=kR3

Q =0 kR3 ds = 0 kR3 4piR2 =4pi0kR5

by second method , Q = dv =  5k00R r4 dr 0pi sin d 02pid =5k0R5 /5 x4 pi =4 pi k 0R5

c) del.E = / 0

del.E = / x(ax2) = 2ax

=0 2ax

so charge density at x=2m, =40 a

at x=5m,

del.E = / x(b) =0

so charge density at x=5m =0

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.