A thin glass rod is bent into a semicircle of radius R.A charge + Q is uniformly distributed along the upper half,and a charge -Q is uniformly distributed along the lower half,as shown in the figure.If R = 10 cm and the electric field E at point P is 4.81 * 10⁴ N/C in -y direction,what is the charge,Q? Point P is at the center of the semicircle.

Question

Quizplus · Accepted Answer

The electric field at point P due to a semicircle of radius R and charge +Q is given by
E1 =

where k is the Coulomb constant, R is the radius of the semicircle, and Q is the charge on the semicircle.

Similarly, the electric field at point P due to a semicircle of radius R and charge -Q is given by
E2 =

Since the two semicircles are symmetric with respect to the x-axis, the net electric field at point P is in the -y direction and is given by the difference of the two electric fields:

E = E1 - E2 =

Substituting the given values of R and E and solving for Q, we get:

Q =

Q ≈ 42 nC

Therefore, the best choice is C.

A Thin Glass Rod Is Bent into a Semicircle of Radius