Final answer:
The question relates to the proportionality of electric-field lines to the magnitude of an electric charge. Since a +20 nC charge is four times the +5 nC charge, it should emit four times the number of electric-field lines, which is 20 field lines.
Step-by-step explanation:
The student is asking about the relationship between electric charge and the number of electric-field lines emanating from that charge. In physics, the number of electric-field lines is proportional to the magnitude of the charge. If a charge of +5 nC produces five electric-field lines, then a charge that is four times greater, such as +20 nC, should produce four times the number of electric-field lines. Therefore, the correct answer would be:
d. 20 field lines
This is because the charge of +20 nC is exactly four times the charge of +5 nC, and consequently, the number of field lines also increases by a factor of four. This explanation directly corresponds to the concept of electric field lines in electrostatics, which visually describe the electric field generated by charges. It is a proportional relationship where the quantity of field lines represents the strength or magnitude of the electric charge.