Electric Field MCQ Homework Help

[Vibhor]

Homework Statement

Homework Equations

The Attempt at a Solution

I believe a) and c) are correct options . Regarding option b) if I find charge q as function of radius , then option b) also seems correct . But if I think in terms of electric field lines then I am not sure about option b) .

Since electric field lines converge at the origin , then suppose if I take a sphere of radius 1 unit centered at say (4,4,4) ,then shouldn't the number of lines entering the sphere be same as that leaving the sphere . Applying Gauss's law the charge enclosed should be zero .

Is convergence of electric field same as convergence of electric field lines ?

Please help me in removing the doubt .

Many Thanks

 

[ehild]

Homework Statement

Homework Equations

The Attempt at a Solution

I believe a) and c) are correct options . Regarding option b) if I find charge q as function of radius , then option b) also seems correct . But if I think in terms of electric field lines then I am not sure about option b) .

Since electric field lines converge at the origin , then suppose if I take a sphere of radius 1 unit centered at say (4,4,4) ,then shouldn't the number of lines entering the sphere be same as that leaving the sphere . Applying Gauss's law the charge enclosed should be zero .

Is convergence of electric field same as convergence of electric field lines ?

Please help me in removing the doubt .

Many Thanks

I would say the electric field points to the origin instead of converging towards it. The electric field is a function of the position, it can converge at a value when approaching the origin. This field converges to zero at the origin.
Can you write the electric field $E(\vec r)$ as function of the position vector ?
You are right, options a) and c) are correct. That also means c) is wrong.
b) is easy to answer if you use the differential form of Gauss theorem. $Div \vec E = \rho(\vec r) /ε_0$ where ρ is the charge density at a given position $\vec r$.
It is not sure that the net flux is zero in case of a closed surface not centered around the origin.

 

[rude man]

Neither (c) nor (d) look right to me.
4πr²ε(100r) = Q ≠ 3e-9 and also ≠ 3e-13?

 

[ehild]

Neither (c) nor (d) look right to me.
4πr²ε(100r) = Q ≠ 3e-9 and also ≠ 3e-13?

Why? C is correct to 3 digits.

 

[rude man]

Why? C is correct to 3 digits.

Right. Quite a coincidence given r = 3 (cm.). But I interpreted the answer 3e-13 as absolute. Shoulkd have done the computation.