A point charge q 1 = -5.8 C is located at the center of a thick conducting shell

Question

A point charge q1 = -5.8 C is located at the center of a thick conducting shell of inner radius a = 2.9 cm and outer radius b = 4.5 cm, The conducting shell has a net charge of q2 = 1.8 C.

1)

What is Ex(P), the value of the x-component of the electric field at point P, located a distance 6.3 cm along the x-axis from q1? N/C

2)

What is Ey(P), the value of the y-component of the electric field at point P, located a distance 6.3 cm along the x-axis from q1?N/C

3)

What is Ex(R), the value of the x-component of the electric field at point R, located a distance 1.45 cm along the y-axis from q1?N/C

4)

What is Ey(R), the value of the y-component of the electric field at point R, located a distance 1.45 cm along the y-axis from q1?N/C

5)

What is b, the surface charge density at the outer edge of the shell?C/m2

6)

What is a, the surface charge density at the inner edge of the shell?C/m2

7)

For how many values of x: (4.5 cm < x < infinity) is it true that Ex = 0? chose one

1)none

2)one

3)more than one

Explanation / Answer

1)

Here , at point P

Ex(P) = k * (q1 + q2)/d^2

Ex(P) = 9*10^9 * 10^-6 *(1.8 - 5.8)/0.063^2

Ex(P) = - 9.07 *10^7 N/C

2)

as electric field is radially inwards

Ey(P) = 0 N/C

3)

Now , at point R ,

as the electric field is radial ,

Ex(R) = 0 N/C

4)

Ey(R) = 9*10^9 * (-5.8 *10^-6)/.0145^2

Ey(R) = -2.48 *10^8 N/C

the y-component of the electric field at point R is -2.48 *10^8 N/C

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