Question

Sketch qualitatively the electric field lines both between and outside two concentric conducting spherical shells when a uniformpositive charge${\mathit{q}}_{\mathbf{1}}$is on the inner shell and a uniform negative charge$\mathbf{-}{\mathit{q}}_{\mathbf{2}}$is on the outer. Consider the cases,${\mathit{q}}_{\mathbf{1}}\mathbf{=}{\mathit{q}}_{\mathbf{2}}$,${\mathit{q}}_{\mathbf{1}}\mathbf{>}{\mathit{q}}_{\mathbf{2}}$ and${\mathit{q}}_{\mathbf{1}}\mathbf{<}{\mathit{q}}_{\mathbf{2}}$.

Short answer

The electric field lines for both between and outside the two concentric conducting spherical shells when a uniform positive charge is placed on the inner shell and a uniform negative charge on the outer shell is sketched.

Step-by-step solution

The given data 

A uniform positive chargeis placed on the inner shell and a uniform negative charge$-q_2$is on the outer shell.

Understanding the concept of electric field lines

The electric field lines are directed from the positive charges toward the negative charges. They never intersect each other because if intersect, then they will have two directions which is not possible.

a) Calculation of sketching the electric field lines for the caseq1=q2 

We note that the symbol is used in the problem statement to mean the absolute valueof the negative charge that resides on the larger shell. The following sketch is for.$q_1=q_2$

b) Calculation of sketching the electric field lines for the caseq1>q2 

Using the concept of the flow of electric field lines and keeping in mind that the positive charge on the inner shell is larger in quantity, the following sketch is for the case,.$q_1>q_2$

q1>q2Step 5: c) Calculation of sketching the electric field lines for the case q1>q2

Using the concept of the flow of electric field lines and keeping in mind that the negative charge on the outer shell is larger in quantity, the following sketch is for the case,$q_1<q_2$.