A line of positive charge is formed into a semicircle of radius R as shown in the fig- ure to the right. The charge per unit length along the semicircle is given by A, and is constant. The total charge on the semicir- cle is Q. R (a) Determine the constant, A, in terms of the Coulomb constant k, total charge Q, and radius R. (b) What is the clectric ficld, E (magnitude and direction), at the origin (the center of curvature)? Note: Recall that the arclength subtended by an angle 0 in radians along a circle of radius R is s = R0. Furthermore, you might find the following integral useful: CT/2 cos e de = 2. 7/2

A line of positive charge is formed into a semicircle of radius R as shown in the fig- ure to the right. The charge per unit length along the semicircle is given by A, and is constant. The total charge on the semicir- cle is Q. R (a) Determine the constant, A, in terms of the Coulomb constant k, total charge Q, and radius R. (b) What is the clectric ficld, E (magnitude and direction), at the origin (the center of curvature)? Note: Recall that the arclength subtended by an angle 0 in radians along a circle of radius R is s = R0. Furthermore, you might find the following integral useful: CT/2 cos e de = 2. 7/2