A metal sphere hangs from a string and has 2 kg of mass. The sphere has a charge

Question

A metal sphere hangs from a string and has 2 kg of mass. The sphere has a charge of +6.9 pC. A uniform electric field is turned on and directed to the right. Which way does the sphere move? What is the electric force on the metal sphere if the magnitude of the electric field is 106 N/C? How does force relate to the electric field? Did you convert all your units to SI? N When the sphere reaches equilibrium, what is the angle that the string makes with the vertical axis (assuming the same electric field as part (b))? If you have two equations for how the tension relates to the electric force and gravity, how can you use them to find the angle of the string?

Explanation / Answer

Here,

a) the sphere will move in the direction of field , right

b) for the electric force

electric force acting on sphere = q * E

electric force acting on sphere = 6.9 *10^-6 * 10^6

electric force acting on sphere = 6.9 N

c) weight , w = 2 * 9.8

w = 19.6 N

for the angle theta

tan(theta) = 6.9/19.6

theta = 19.4 degree

the angle of string with the vertical is 19.4 degree

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