Two 2.0 g spheres are suspended by 10.0 cm long light strings. A uniform electric field is applied in the x direction. If the spheres have charges of -5.0 10-8 C and +5.0 10-8 C, determine the electric field intensity that enables the spheres to be in equilibrium at = 10°.

To determine the electric field intensity that enables the spheres to be in equilibrium, we need to consider the forces acting on each sphere.

First, let's calculate the gravitational force acting on each sphere. The weight of an object can be calculated using the formula:

Weight = mass × acceleration due to gravity.

Given that each sphere has a mass of 2.0 g (0.002 kg) and the acceleration due to gravity is approximately 9.8 m/s², the weight of each sphere is:

Weight = 0.002 kg × 9.8 m/s² = 0.0196 N.

Since the spheres are in equilibrium, the electric force experienced by each sphere must counterbalance the gravitational force acting on it. The electric force between two charged objects is given by Coulomb's law, which states:

Electric Force = (k × charge₁ × charge₂) / distance²,

where k is the electrostatic constant (k ≈ 9 × 10^9 N.m²/C²).

For the negative sphere:

Electric Force = (k × charge of negative sphere × charge of positive sphere) / distance²,
= (9 × 10^9 N.m²/C² × (-5.0 × 10^-8 C) × (5.0 × 10^-8 C)) / (0.1 m)²,
= -225 N.

For the positive sphere, the electric force will be identical in magnitude but opposite in direction (+225 N).

Now, let's find the electric field intensity (E) that will result in an electric force of 225 N. The electric force experienced by an object in an electric field is given by the formula:

Electric Force = charge × electric field intensity.

For the negative sphere:

-225 N = (-5.0 × 10^-8 C) × E,
E = -225 N / (-5.0 × 10^-8 C) ≈ 4.5 × 10^9 N/C.

For the positive sphere, the electric field intensity will have the same magnitude but opposite sign (-4.5 × 10^9 N/C).

Therefore, the electric field intensity required to maintain the spheres in equilibrium at an angle of 10° is approximately 4.5 × 10^9 N/C in the x-direction.

Mass of sphere = 2*10^-3 kg

Weight of sohere = 9.8*2 *10^-3 = 1.96 *10^-2 N
Force to hold at 10deg = 1.96*10^-2 * tan 10
= 3.45 *10^-3 N
= E * q
so
E = 3.45 *10^-3 / 5 *10^-8

6.91*10^4 N/C

Follow the same process

F:Static electricity force which the sphere receives
F=qE+kq^2/r^2
(r=8*10^(-2)×sin11°×2)
sin11°=0.190

the weight of the sphere: mg
(=3*10^(-3)×9.8N)

F/mg=tan11°(=0.194)
F=tan11°*mg
qE-kq^2/r^2= tan11°*mg
E=kq/r^2+tan11°*mg/q

=2.90*10^5+1.90*10^5
=4.80*10^5(N/m)