Five equal negative charges are uniformly spaced in a semicircular arc of radius r₀ with its center at the origin.The charges positions in polar coordinates are given by (r₀,θ_i),where the values of θ_iare 0°,45°,90°,135°,and 180°.At the position (x,y)= (r₀,-r₀)in the 4th quadrant,which statement best describes the direction of the resulting electric field? A)The direction is that of a 4th quadrant angle. B)The direction is that of a 3rd quadrant angle. C)The direction is that of a 1st quadrant angle. D)The direction is that of a 2nd quadrant angle.

Question

Quizplus · Accepted Answer

The electric field at the point (r, -r) due to the five charges will have components in both the x and y directions. The x-component of the electric field will be zero due to the symmetry of the charges, while the y-component will be the sum of the y-components of the individual electric fields due to each charge. 
Since the charges are equally spaced in a semicircular arc, the y-components of the electric fields due to the charges at 0° and 180° will cancel each other out, as will the y-components of the electric fields due to the charges at 45° and 135°. The only remaining y-component will be from the charge at 90°, which will point downwards in the negative y-direction. 
Thus, the resulting electric field at the point (r, -r) will be in the 4th quadrant, with a direction of a 2nd quadrant angle (i.e. downwards and to the right). Therefore, the correct answer is choice D.

Five Equal Negative Charges Are Uniformly Spaced in a Semicircular