A charged plane has an unknown charge per unit area ?. A 10 cm long string is at

Question

A charged plane has an unknown charge per unit area ?. A 10 cm long string is attached to the wall. It makes a 30o angle with the wall. At the end of the string is a 1g mass with an electric charge of 10?C. The mass is at rest. Answer the questions below. a) Use Gauss?s Law to show that the electric field to the right of the wall has magnitude E = ? /2?o b) Use the fact that the mass is at rest to find the value of ?.

A charged plane has an unknown charge per unit area ?. A 10 cm long string is attached to the wall. It makes a 30o angle with the wall. At the end of the string is a 1g mass with an electric charge of 10?C. The mass is at rest. Answer the questions below. a) Use Gauss?s Law to show that the electric field to the right of the wall has magnitude E = ? /2?o b) Use the fact that the mass is at rest to find the value of ?.

Explanation / Answer

consider a cylinderical closed surface with its axis perpendicual to the plate
its a gausian surafcae n has a charge enclosed = r^2 * x

so E AT A DISTANCE D FROM THE PLATE IS EQAUL TO = R^2 *X/2r^2 = X/2

TCOS 30 = .001 g

t= 0.0115

and t sin 30 = 10 *x/2

so x= 0.0115 *0.5*2/10

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