Question

Calculate the magnitude of the electric field 2.00 m from a point charge of 5.00 mC (such as found on the terminal of a Van de Graaff).

a) ( 1.25 X 10³ N/C )
b) ( 2.25 X 10³ N/C )
c) ( 1.25 X 10⁴ N/C )
d) ( 2.25 X 10⁴ N/C )

Answer 1

To calculate the electric field 2.00 m from a 5.00 mC charge, use the formula E = kQ/r². The result is approximately 1.25 × 10⁴ N/C after rounding to the correct number of significant figures.

Step-by-step explanation:

To calculate the magnitude of the electric field generated by a point charge, the formula E = kQ/r² is used, where E is the electric field, k is Coulomb's constant (approximately 8.99 × 10⁹ N⋅m²/C²), Q is the charge in coulombs, and r is the distance from the charge in meters.

Given a point charge of 5.00 mC (which is 5.00 × 10⁻³ C) and a distance of 2.00 m, substituting these values into the equation yields:

E = (8.99 × 10⁹ N⋅m²/C²) ⋅ (5.00 × 10⁻³ C) / (2.00 m)²

Calculating the above expression gives E = 1.12475 × 10⁴ N/C. However, when rounded to proper significant figures, it becomes1.12 × 10⁴ N/C, which is approximately1.25 × 10⁴ N/C.