Question

q1

Recitation 22B-Turn in your work at the end of the period 

Problem 1

 A cube of side \(2.0 \mathrm{~m}\) sits ou the \(x y\) plane with one comer at the origin. There is a nom-aniform clectnic field given by \(\vec{E}=\left[\left(4.0 \times 10^{2}\right) \mathrm{x}+350\right] \mathrm{NC} i\), where \(x\) is in meters. Calculate

(a) the net electric flux through the cube. (Hint Add the flux through each surface) \(32 \mathrm{kN} \cdot \mathrm{m}^{2} / \mathrm{C}\).

(b) the net charge enclosed. \(0.28 \mathrm{pC}\)

Problem 2 

A hollow insulating sphere has an inner radius a and outer radius \(b\). It has a umiform charge density \(\rho\). Derive expressions for the maguitude of the electric field in the following regioms [Final answers aot givea]

(a) \(0<r \leq a\).

(b) \(a \leq r \leq b\).

(c) \(r \geq b\)

Answer 1

Since electric field is only in x direction so flux will be only through faces which are parallel to y-z plane.One such plane is passing through x=0 and other through x=2.

Flux through other faces of cube will be zero.Because flux is dot product of electric field and area vector.And through other faces area and electric field vectors are perpendicular.