Question

As shown in the figure on the right, a small bead with a mass of 4.00 grams and a charge of +10.0 $\mu$ C is suspended on a non-conducting 120.0 cm long thread at an angle of 35^o from the center of a very large vertical flat, non-conducting plate with a uniform, but unknown, surface charge density. What is the charge density on the plate in C/m² ? Given: $\varepsilon$ ₀ = 8.854 x 10^-12 C2 /N-m2 ANSWER: $\sigma$ = 4.86 x 10^-8 C/m2

Answer 1

Electric field due to the plate, E_p = σ/2ε_o

Let T be the tension in the thread.

Vertical force balance for the bead:

Tcosθ = mg

Horizontal force balance for the bead:

Tsinθ = (σ/2ε_o)q

Dividing the second equation by first, we get,

tanθ = σq/2ε_omg

=> σ = 2ε_omgtanθ/q

=> σ = 2 * (8.854 * 10^-12) * (4 * 10^-3) * 9.81 * tan35^o / (10 * 10^-6) = 4.87 * 10^-8 C/m²