Question

Problem 2 A total charge Q is uniformly distributed on a thin ring of radius R which lies in the x-y plane, with its center at the origin. Consider point P on the z-axis, which is a distance d from the origin. (a) Determine the direction of the electric field at point P (i.e., is it pointing in the x, y, or z direction?). Make an argument from symmetry to justify your answer. $\vec{E} = \int d\vec{E}$ The E-Field points only in the z direction. This is because the x & y E-field components cancel out. For every x/y component, there is a -x/-y component also acting on point P that cancels out its direction. (b) Find an expression for the electric field at point P. Your answer should be a symbolic expression that only depends on the variables k, Q, R, and d. Hint: you will have to break the line up into infinitesimal charge elements ($dQ$) and then integrate over the elements. There is more space on the next page to complete your work.

          Problem 2
A total charge Q is uniformly distributed on a thin ring of radius R which lies in the x-y plane,
with its center at the origin. Consider point P on the z-axis, which is a distance d from the origin.
(a) Determine the direction of the electric field at point P (i.e., is it pointing in the x, y,
or z direction?). Make an argument from symmetry to justify your answer.
$\vec{E} = \int d\vec{E}$
The E-Field points only in the z
direction. This is because the
x & y E-field components cancel out.
For every x/y component, there is a -x/-y
component also acting on point P
that cancels out its direction.
(b) Find an expression for the electric field at point P. Your answer should be a symbolic
expression that only depends on the variables k, Q, R, and d. Hint: you will have to
break the line up into infinitesimal charge elements ($dQ$) and then integrate over the
elements. There is more space on the next page to complete your work.

Problem 2
A total charge Q is uniformly distributed on a thin ring of radius R which lies in the x-y plane,
with its center at the origin. Consider point P on the z-axis, which is a distance d from the origin.
(a) Determine the direction of the electric field at point P (i.e., is it pointing in the x, y,
or z direction?). Make an argument from symmetry to justify your answer.
E⃗ = ∫ dE⃗
The E-Field points only in the z
direction. This is because the
x y E-field components cancel out.
For every x/y component, there is a -x/-y
component also acting on point P
that cancels out its direction.
(b) Find an expression for the electric field at point P. Your answer should be a symbolic
expression that only depends on the variables k, Q, R, and d. Hint: you will have to
break the line up into infinitesimal charge elements (dQ) and then integrate over the
elements. There is more space on the next page to complete your work.

Added by Kevin A.

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