Q1:

With a line charge along z-axis the field intensity is E = ; which of the following figure shows an exact field distribution?

The given figure fails to show the symmetry with respect to Φ. The figure shows symmetry with respect to f, also the length of arrow is decreasing away from the charge shows that magnitude E is decreasing away from line charge. But problem with this figure is longest lines must be shown in most crowded region. Here we use lines of fixed segments but different thickness. But this attempt also makes the region crowded near origin. This figure shows compromise. A symmetrical distribution of lines (at every 45°) shows azimuthal symmetry and arrowheads show direction.