Hello I need help with this homeowrk problem please! A small sphere with mass 2.

Question

Hello I need help with this homeowrk problem please!

A small sphere with mass 2.25g hangs by a light massless thread between two vertical plates separated by 2.50cm. The plates have uniform surface charge densities +sigma and -sigma. The charge on the sphere is -6.5muC. Determine the potential difference between the two plates such that the thread makes an angle of 22.5degree with respect to the vertical. Also determine the magnitude and direction of the electric field and the magnitude of the surface charge density, sigma.

Explanation / Answer

in the equilibrium net force is zero in x and y directions.

let T is the tension in the string

let E is the lectric filed.

Fnety = 0

T*cos(22.5) = m*g

T = m*g/(cos(22.5)

= 2.25*10^-3*9.8/cos(22.5)

= 2.387*10^-2 N

Fnetx = 0

T*sin(22.5) - q*E = 0

==> E = T*sin(22.5)/q

= 2.387*10^-2*sin(22.5)/6.5*10^-6

= 1405 N/c <<<<<<<<<-Answer

we know

E = sigma/espilon

sigma = E*epsilon

= 1405*8.854*10^-12

= 1.24*10^-8 C/m^2 <<<<<<-Answer

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