Question

A point charge q1 -6.4 HC is located at the center of a thick conducting shell of inner radius a = 2.7 cm and outer radius b-4.2 cm, The conducting shell has a net charge of q2 1.4 HC Ay 1) What is Ex(P), the value of the x-component of the electric field at point P, located a distance 8.2 cm along the x-axis from q1? N/C Submit Your submissions: | 0 Computed value: 0Submitted: Sunday, January 27 at 10:18 PM Feedback: 2) What is Ey(P), the value of the y-component of the electric field at point located a distance 8.2 cm along the x-axis from q1? N/C Submit

Answer 1

Given,

point charge, q₁ = -6.4 $\dpi{100} \mu$C

Net charge of conducting shell, q₂ = 1.4 $\dpi{100} \mu$C

Gaussian surface for the shell must be a sphere.

Distance from origin, R = 8.2 cm = 0.082 m

Now,

Net charge enclosed, Q _en = q₁ + q₂ = -6.4 $\dpi{100} \mu$C + 1.4 $\dpi{100} \mu$C

                                           = -5 $\dpi{100} \mu$C

Now,

according to Gauss's Law,

$\dpi{100} \oint E.dA = Q_{en} / \epsilon _{0}$

=> E * A = Q _en / $\dpi{100} \epsilon _{0}$

=> E * (4*$\dpi{100} \pi$*R²) = -5 $\dpi{100} \mu$C / $\dpi{100} \epsilon _{0}$

=> E = -5 $\dpi{100} \mu$C / ( $\dpi{100} \epsilon _{0}$ *4*$\dpi{100} \pi$*R²)

         = - 5 * 10^-6 / (8.85 * 10^-12 * 4 * 3.14 * 0.082 * 0.082)

         = -6.7 * 10⁶ N/C

Negative sign shows direction is inwards, i.e in negative X direction.

(2)

Since, direction of electric field is radially inwards, thus, there is no component of electric field along y-axis at point P.

Thus, answer is zero