A uniformly charged insulating rod of length 19.5 cm is bent into the shape of a semicircle as shown in the figure below. The rod has a total charge of −7.50 µC.A rectangular rod is bent into the shape of the left half of a circle centered about a point O.(a) Find the magnitude of the electric field at O, the center of the semicircle.(b) Find the direction of the electric field at O, the center of the semicircle. (a) Let A be the charge per unit length and let r be the radius of the semicircular ring. From the diagram, we see thatdq = Arde.The field created by the charge dq has magnitudekda kArdedE =r2r2In component form, E, = 0 (from symmetry) and for the x component, we havedE, = dE cos e.Integrating dE, over all of the charge, we have the following.kar cos 8ka (T/2Ex =de =cos e de-n/2dE, =r22ksin%3D--피/2For the total charge, we have Q = Ae, where e is the length of the rod. The rod has been bent into a semicircle so ar = l. For the radius, we have r = e/n. Substituting these expressions for 2 and r, wehave the following.2nk QEx =2n(8.99 x 109 N.|x 107 N/Cm) A uniformly charged insulating rod of length 19.5 cm is bent into the shape of a semicircle as shown in the figure below. The rod has a total charge of -7.50 µC.(a) Find the magnitude of the electric field at O, the center of the semicircle.(b) Find the direction of the electric field at o, the center of the semicircle.

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A uniformly charged insulating rod of length 19.5 cm is bent into the shape of a semicircle as shown in the figure below. The rod has a total charge of −7.50 µC. A rectangular rod is bent into the shape of the left half of a circle centered about a point O. (a) Find the magnitude of the electric field at O, the center of the semicircle. (b) Find the direction of the electric field at O, the center of the semicircle.

A uniformly charged insulating rod of length 19.5 cm is bent into the shape of a semicircle as shown in the figure below. The rod has a total charge of −7.50 µC. A rectangular rod is bent into the shape of the left half of a circle centered about a point O. (a) Find the magnitude of the electric field at O, the center of the semicircle. (b) Find the direction of the electric field at O, the center of the semicircle.

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