physics Two small spheres?

Question

Two small spheres, each of mass 3.00 g, are suspended by light strings 10.0 cm in length (Fig. P23.62). A uniform electric field is applied in the x direction. The spheres have charges equal to -3.00 10-8 C and +3.00 10-8 C. Determine the electric field that enables the spheres to be in equilibrium at an angle of = 12.0°.

Answer 1

The electrostatic repulsive force and the part of gravity acting in the opposite direction must be equal to reach this equilibrium.

gravitional force,
F = Gm1m2/d^2
here, m1 = m2 = m = 3 g
F = G(m/d)^2 .......................(1)

the component of this force acting horizontally is Fsin(A/2). Here A = 12 degree.

the effective component of gravity = G(m/d)^2 * sin(A/2)..........(2)

the electrostatic force = qE
here q1 = q2 = q = 3*10^(-8); [ just consider the value, without +/- sign]


electrostatic force = qE......................................(3)

equation equation (2) and (3)

G(m/d)^2 * sin(A/2) = qE

therefore, the electric field, E is equal to

E = G/q (m/d)^2 *sin(A/2)


just put the values in and do the calculation.You should get the right result. Put m in kg, q in coulomb, d in meters and E will be in N/C.

Answer 2

This looks like an assignment question for 1st year Physics. This problem is not hard and I am sure you can find examples in the text book.