Question

A long cylindrical shell carries positive surface charge $\sigma$ in the upper half and negative surface charge $- \sigma$ in the lower half. The electric field lies around the cylinder will look like as:

Answer 1

An electric field line is a path, straight or curved in electric field, such that tangent to it at any point gives the direction of electric field intensity at that point. Electric field lines form continuous curves and No two electric field lines intersect each other.

Complete Step by Step Answer:
We know that the electric field lines due to a positive point charge are represented

These are directly radially ${Q_{outwards}}$ . The lines of force extend to infinity.
The electric field lines due to negative point charge are represented as:

Lines of force are directed radially inwards.
According to question, the cylindrical shell with positive charge $\sigma$ and negative charge $- \sigma$represented as:

The electric field lines along this cylindrical shell can be represented as:

From electric field lines, we know that field lines should originate from positive charge and terminate to negative charge.
As from properties of electric field lines we know the
Electric field lines form continuous curves
No two electric field lines intersect each other.
Hence, the diagram represents the electric field lines along a long cylindrical shell.

Note: The magnitude of the field is represented by the density of field lines. Near the charge, lines are closer so that the density of field lines is more and hence electric field $\overrightarrow E$ is stronger near the charge. Away from the charge, the field lines are well separated, the density of field lines is smaller and electric field $\overrightarrow E$ is weaker away from the charge.