A wall has a negative charge distribution pro- ducing a uniform horizontal elect

Question

A wall has a negative charge distribution pro- ducing a uniform horizontal electric field. A small plastic ball of mass 0.0209 kg, carrying charge of-99 C, is suspended by an un- charged, nonconducting thread 0.26 m long The thread is attached to the wall and the all hangs in equilibrium in the electric and gravitational fields, as shown. (out) 0.0209 kg Find the magnitude of the electric field at the ball's location due to the charged wall. Assume the electric force on the ball has a magnitude of 0.0391 N. The acceleration due to gravity is 9.8 m/s Answer in units of N/C.

Explanation / Answer

as we know, electric force=electric field*charge

==>electric field magnitude=electric force/electric charge
=0.0391/(99*10^(-6))=394.95 N/C

as the charge is moving away from the wall , the electric field will be along -ve x direction

(so that force acting on the negative charge will be along +ve x direction)

part b:

let tension in the string be T and angle made by the string with vertical be theta

then balancing vertical forces:

T*cos(theta)=weight of the ball=0.0209*9.8

==>T*cos(theta)=0.20482...(1)

balancing horizontal forces:

T*sin(theta)=electrical force

==>T*sin(theta)=0.0391...(2)

dividing equation 2 by equation 1,

tan(theta)=0.1909

==>theta=10.8077 degrees

hence if perpendicular distance from the wall to center of the ball is d,

then sin(theta)=d/0.26

==>0.26*sin(10.8077)=0.04875 m

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