Question

A 3.6 g aluminum foil ball with a charge of +4.7×10−9 C is suspended on a string in a uniform horizontal E⃗ field. The string deviates to the right and makes an angle of 30∘ with the vertical. Determine the magnitude of the electric field.

Answer 1

Using Force balance on foil ball:

Suppose tension in thread is T and angle with the vertical is

Now Using force balance on ball In vertical direction

Ty = W

T*cos = m*g

In horizontal direction

Tx = Fe

T*sin = q*E

dividing both equation:

sin /cos = q*E/(m*g)

tan = q*E/(m*g)

E = (m*g*tan )/q

Using given values:

E = (3.6*10^-3*9.81*tan 30 deg)/(4.7*10^-9) = 4338234 N/C

In two significant figures

E = 4.3*10^6 N/C = magnitude of electric field

Let me know if you've any query.