Three small spherical charges lie on a circle with radius 30$\mathrm{.}0$ cm$.$ The first sphere has a charge $+30.0$ C and lies at $4$5 degrees counter clockwise $($CCW$)$ relative to $+$x axis. The second has charge $+15.0$ C and lies at $140$ degrees CCW to the $+$x axis; the third charge $-35.0$ C lies at $280$ degrees CCW to the $+$ x axis.

a$.$ Draw a physics diagram of the problem. Be sure to draw the field vector for each charge and the total field, at the center of the circle.

b$.$ Find the electric field vector $($in component form$)$ for each charge at the center of the circle. Then compute the total electric field vector at the origin.