Question

A small sphere with mass 2.60 g hangs by a thread between two large parallel vertical plates 5.00 cm apart (Figure 1) . The plates are insulating and have uniform surface charge densities +σ and −σ. The charge on the sphere is q = 8.40×10−6 C . Part A What potential difference between the plates will cause the thread to assume an angle of 30.0∘ with the vertical?

Answer 1

By the sum of forces in the vertical direction, the weight = the vertical component of the tension in the string

mg = Tcos(30)

(.0026)(9.8) = T(cos 30)

T = .0294 N

In the horizontal, the Electric Field applies a force balanced by the horizontal component of the tension

qE = Tsin(30)

(8.40*10^-6)(E) = (.0294)(sin 30)

E = 1750 V/m

Finally apply V = Ed

V = (1750)(.05)

V = 87.5 V,