Final answer:
The magnitude of the electric field at a distance of 2.0 cm from the center of a small glass bead charged to 8.0 nC is calculated using the formula E = kQ/r², resulting in 3.596×10µ N/C.
Step-by-step explanation:
The student's question involves calculating the magnitude of the electric field generated by a small glass bead charged to 8.0 nC located 2.0 cm from the center of the bead. The formula to calculate the electric field (E) due to a point charge (Q) at a distance (r) is given by:
E = kQ/r²
Here, k is the Coulomb's constant (8.99×10¹ N·m²/C²), Q is the charge of the bead (8.0 nC = 8.0×10⁻⁹ C), and r is the distance from the charge (2.0 cm = 0.02 m). Plugging in these values,
E = (8.99×10¹ N·m²/C²) × (8.0×10⁻⁹ C) / (0.02 m)²
E = 1.798×10¹ N·m²/C² × 8.0×10⁻⁹ C / 4.00×10⁻⁴ m²
E = 3.596×10µ N/C
Thus, the magnitude of the electric field at 2.0 cm from the center of the bead is 3.596×10µ N/C.