Question

The electric flux through a spherical surface is 1.4 ✕ 105 N · m2/C. What is the net charge (in C) enclosed by the surface?

Answer 1

Using Gauss's law, the net charge enclosed by a spherical surface with an electric flux of 1.4 × 10^5 N · m^2/C is calculated to be 1.24 × 10^-6 C.

Step-by-step explanation:

The electric flux through a spherical surface is 1.4 × 105 N · m2/C. To find the net charge enclosed by the surface, we use Gauss's law, which states that the electric flux (Φ) through a closed surface is equal to the net charge (qenc) inside the surface divided by the vacuum permittivity (ε0).

The formula derived from Gauss's law is:

qenc = Φ ε0

Where Φ is the electric flux and ε0 (epsilon naught) is the vacuum permittivity constant, approximately 8.85 × 10-12 C2/N · m2. Substituting the values, we get:

qenc = (1.4 × 105 N · m2/C) × (8.85 × 10-12 C2/N · m2) = 1.24 × 10-6 C

The net charge enclosed by the spherical surface is 1.24 × 10-6 C.

Answer 2

The value is
`Q_(net) =  1.239 *10^(-6) \  C`

Step-by-step explanation:

From the question we are told that

The electric flux is
`\Phi =  1.4*10^(5) \  N\cdot m^2/C`

Generally the net charge is mathematically represented as

`Q_(net) =  \Phi *  \epsilon_o`

Here
`\epsilon_o` is the permetivity of free space with value

`\epsilon_o =  8.85*10^(-12)  \  \  m^(-3) \cdot kg^(-1)\cdot  s^4 \cdot A^2`

So

`Q_(net) =  1.4*10^5 *  8.85*10^(-12)`

=>
`Q_(net) =  1.239 *10^(-6) \  C`