Two identical small insulating spheres carry equal positive charges and hang from a…

PHYSICS · Subjective · AP · Physics 2: Algebra-based · Electric Force Field and Potential · Electric Force Field and Potential

Problem

Two identical small insulating spheres carry equal positive charges and hang from a common fixed point by two light, non-conducting strings of length

30\,\text{cm}

. In air, each string makes an angle of

12^{\circ}

with the vertical. After the apparatus is completely immersed in an insulating liquid, the angle decreases to

5.0^{\circ}

. Assuming the charges remain constant and the spheres are small compared with their separation, determine the dielectric constant

\kappa

of the liquid.