Question

A thin, circular disk of radius 30.0 cm is oriented in the yz-plane with its center at the origin. The disk carries a total charge of +3.00 ?C distributed uniformly over its surface. Calculate the magnitude of the electric field due to the disk at the point x=15.0 cm along the x-axis. (?0=8.85×10?12 C

a. 9.95×109 N/C
b. 4.98×109 N/C
c. 3.31×109 N/C
d. 2.49×109 N/C
e. 1.99×109 N/C

Answer 1

Answer:

option C

Explanation:

given,

radius = 30 cm

charge = + 3 μC

x = 15 cm

ε₀ = 8.85 x 10⁻¹² C²/N.m²

Electric on the x-axis of disk

$E = \dfrac{Q}{2\epsilon_0 \pi R^2}(1-\dfrac{x}{\sqrt{x^2+R^2}})$

$E = \dfrac{3 \times 10^{-6}}{2\times 8.85 \times 10^{-12} \pi\times 0.3^2}(1-\dfrac{0.15}{\sqrt{0.15^2+0.3^2}})$

E = 3.31 x 10⁵ N/C

Hence, the correct answer is option C