A charged cork ball is suspended on a light string in the presence of a uniform electric field E~ = (2.2 × 105 N/C)ˆı + (3.6 × 105 N/C) ˆ . The ball is in equilibrium in the field. Find the charge on the ball. The acceleration due to gravity is 9.8 m/s 2 . Answer in units of nC.

Complete Question:

A charged cork ball is suspended on a light string in the presence of a uniform electric field E~ = (2.2 × 105 N/C) i + (3.6 × 105 N/C) j . The ball is in equilibrium in the field. Find the charge on the ball. The acceleration due to gravity is 9.8 m/s 2. The mass of the ball is 0.7g. The length of the string is 1.4m and at an angle of 37 degrees from the center. Answer in units of nC.

The charge on the ball is 0.1052 nC

Explanation:

Given;

vertical component of the Electric field, Ey = (3.6 × 10⁵ N/C)

horizontal component of the Electric field, Ex =  (2.2 × 10⁵ N/C)

If the cork ball is in equilibrium, then the upward force is equal to the downward force.

Also sum of all the forces acting on the cork ball is zero.

From equation (i)

Tsin(37) = (2.2 × 10⁵)q

Substitute equation (iii) into equation (ii) and solve for q

Therefore, the charge on the ball is 0.1052 nC

0.11 m/s and 0.28 m/s should be correct