Question

0 A small sphere is suspended from a string in a uniform electric field shown by arrows, making an angle 0=25° with the vertical. If the mass of the sphere is 3 grams and it has a charge of 4 nC, what is the magnitude of the electric field? 3.43 x 106 N/C 3.43 N/C 0.35 N/C 15.8 x 106 N/C O 3.5 x 105 N/C 15.8 N/C

Answer 1

The vertical component of tension (upwards) = T*cos($\theta$)

The horizontal component of tension (left) = T*sin($\theta$)

The force on right side = qE

Downward force = mg

hence from force balance,

T*cos($\theta$) = mg and

T*sin($\theta$) = qE

dividing both the equations

tan($\theta$) = qE/mg

E= mg*tan($\theta$)/q

E = 0.003*9.81*tan(25)/(4*10^-9)

E = 3.43*10⁶ N/C