Question

A point charge is located at the center of a thin spherical conducting shell of inner and outer radii r1 and r2, respectively. A second thin spherical conducting shell of inner and outer radii R1 and R2, respectively, is concentric with the first shell. The flux is as follows for the different regions of this arrangement.

Φ = −10.3 ✕ 103 N · m2/C for r < r1Φ = 0 for r1 < r < r2Φ = 36.8 ✕ 103 N · m2/C for r2 < r < R1Φ = 0 for R1 < r < R2Φ = −36.8 ✕ 103 N · m2/C for r > R2

Answer 1

Complete Question

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Answer:

The point charge is
`Q_z = -0.0912 \ \mu C`

The inner shell is
`Q_t = 0.4168 \ \mu C`

The outer shell is
`Q_w = -0.6514 \ \mu C`

Step-by-step explanation:

From the question we are told that

The inner radius of thin first spherical conducting shell is
`r_1`

The outer radius of thin first spherical conducting shell is
`r_2`

The inner radius of second thin spherical conducting shell is
`R_1`

The outer radius of second thin spherical conducting shell is
`R_2`

The magnetic flux for different region is
`\phi = -10.3 *10^3 N\cdot m^2 /C \ for \ r < r_1`

The magnetic flux for first shell is
`\phi = 36 * 10^3 N \cdot m^2 /C \ for \ r_2 < r <R_1`

The magnetic flux for second shell is
`\phi = -36 * 10^3 N \cdot m^2 /C \ for \ r <R_1`

The magnitude of the point charge is mathematically represented as

`Q_z = \ \phi_z * \epsilon _o`

`Q_z = -10.3*10^(3) * 8.85 *10^(-12)`

`Q_z = -9.115*10^(-8) \ C`

`Q_z = -0.0912 \ \mu C`

Considering the inner shell

`Q_a = \phi_a * \epsilon _o`

=>
`Q_a = 36 .8 * 10^3 * 8.85*10^(-12)`

`Q_a = 32.56*10^(-8) \ C`

`Q_a =0.326} \ \mu C`

Charge on the inner shell is

`Q_t = Q_a - Q_z`

`Q_t = 0.326} \ \mu - ( -0.0912 \ \mu)`

`Q_t = 0.4168 \ \mu C`

Considering the outer shell

`Q_y = \phi_y * \epsilon_o`

=>
`Q_y = -36.8 *10^(3) * 8.85*10^(-12)`

`Q_y = -32.56*10^(-8) \ C`

`Q_y = - 0.326} \ \mu C`

Charge on the outer shell is

`Q_w = Q_y - Q_z`

`Q_w =- 0.326} \ \mu - ( -0.0912 \ \mu)`

`Q_w = -0.6514 \ \mu C`