Final answer:
To sketch electric field and equipotential lines around point charges, consider the magnitude and sign of each charge, with field lines indicating the force on a positive test charge. Density of field lines corresponds to electric field strength, and equipotential lines are perpendicular to field lines and closer together where the potential is higher.
Step-by-step explanation:
The student's question pertains to the electric field lines and equipotential lines around point charges. To address the question:
- Equipotential lines are imaginary lines in space where potential difference between any two points is zero. In the vicinity of point charges, these lines are perpendicular to electric field lines.
- When sketching electric field lines around two charges, factor in the magnitude and sign of each charge. For instance, a positive test charge would move away from a positive charge and towards a negative charge because electric field lines indicate the direction of force on a positive test charge.
- The density of field lines indicates the strength of the electric field: closer to the charge, the field is stronger, hence more concentrated field lines.
- For two like charges (e.g., +20 µC and +20 µC), the electric field lines repel each other, while for two opposite charges (e.g., +20 µC and -30 µC), the lines begin at the positive charge and end at the negative charge.
- In a scenario where one charge has a greater magnitude than the other, the electric field lines are denser around the larger charge, showing a stronger electric field in that region.
Considering a case where you have two charges q1 and q2, with q1 being four times q2, you would sketch the electric field lines originating from q1 and curving towards q2, with lines being more concentrated around q1.
As for direction of increasing potential, it is towards the positive charge or away from the negative charge in a field map, and so equipotential lines are closer together near the positive charge.