Quantitative Nature of Electric Charges?

📌 CONCEPT: The electric charge distribution and field lines on the surface of isolated conducting spheres are determined by the magnitude and sign of the charge on the sphere.

📐 RULE / FORMULA: The electric field lines emerge from positive charges and enter into negative charges, and the density of these lines is directly proportional to the magnitude of the charge.

💡 WORKED EXAMPLE: Consider two identical conducting spheres, one with a positive charge of +q and the other with a negative charge of -q. The electric field lines on the surface of the positively charged sphere will emerge radially outward, while those on the surface of the negatively charged sphere will enter radially inward. The density of the field lines on both spheres will be the same, indicating that the electric field is directly proportional to the magnitude of the charge.

⚠️ COMMON MISTAKE: Students often mistakenly assume that the electric field lines will be in the same direction on both spheres, when in fact they will be opposite in direction, depending on the sign of the charge.