In the figure a small, nonconducting ball of mass m = 0.82 mg and charge q = 2.0

Question

In the figure a small, nonconducting ball of mass m = 0.82 mg and charge q = 2.0 × 10-8 C (distributed uniformly through its volume) hangs from an insulating thread that makes an angle = 25° with a vertical, uniformly charged nonconducting sheet (shown in cross section). 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 of the sheet.

In he gure a small nonconducting ball o na s 1-0 82 mu and argu -2.0 10 s C distributed unif rmly hrough its lume hangs rom ari Insula rig read hat makes an angle e Coreidering the gravitational force on the ball and assuming the sheet extends far verticely and into and out of the page, calculate the surface charge derisity o of the sheet. 250 with a vertical, uniformly charged nonconductin sheet shown iri cross section Number the tolerance is +/-296 Click if you would like to Show Work for this question: en Show Work Units

Explanation / Answer

Here Tension balances both Electrostatic Force as well as Gravitational Force.

Tsin theta = Fe

T cos theta = Fg

So tan theta = Fe/Fg

tan 25 degree = qE/mg

E = mg tan 25 degree /q

= 0.82e-6*9.8* tan 25 degree /2e-8

= 187.36 N/C

Electric field due to sheet of charge = sigma /2eo

sigma = 2e0*E

= 2* 8.85e-12 *187.36

= 3.316*10^-9 C/m^2 Answer

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