In the following figure, a small, nonconducting ball of mass m = 1.0 mg and char

Question

In the following figure, a small, nonconducting ball of mass m = 1.0 mg and charge q = 2.0 Times 10^-8 C (distributed uniformly through its volume) hangs from an insulating thread that makes an angle theta = 30 degree with a vertical, uniformly charged (positive) nonconducting sheet (shown in cross section). [Add to the diagram above this text] Considering the gravitational force on the ball and assuming the sheet extends far vertically and into and out of the page, calculate the surface charge density sigma of the sheet. m = 1.0 mg q = 2.0 Times 10^-8 C theta = 30 degree We are to solve for the surface charge density

Explanation / Answer

On the ball there are 3 forces acting on it.

Tension force T. Having x component Tcos30 and y component Tsin30

The electric force as Fe=qE

and gravitational force Fg=mg

no balancing the forces along x and y component we get,

Tcos30 = mg

T=mg/cos30 = 1*10-6*9.8/cos30 = 1.13*10-5N

Also, Tsin30=qE

Hence E= Tsin30/q = 1.13*10-5*sin30/2*10-8 = 283N/C

The electric field for nonconducting sheet of infinite length = E=2k

hence charge density = E/2 k =  283N/ 2..9*109 = 5*10-9 C/m2 = 5nC/m2

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