PHYSICS 7D Study Guide - Quiz Guide: Electric Field, Electric Potential

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PHYSICS 7D Full Course Notes

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Id: in a region of space, the electric potential is given by v(x,y) = ay2 + Bxy cx2 : calculate the x-component of the electric field. E = - by + 2 cx: calculate the y-component of the electric field. E = - 2ay bx: a point charge with charge q1 = 2 c is held stationary at the origin. Id: in a region of space, the electric potential is given by v(x,y) = ax2 + Bxy cy2 : calculate the x-component of the electric field. E = - 2ax - by: calculate the y-component of the electric field. E = -bx + 2cy: calculate the electric potential at the center of an equilateral triangle with sides of length l = 0. 5 m and a charge q = 5 c placed at each vertex of the triangle. Id: a point charge with charge q1 = 3 c is held stationary at the origin.

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Figure 1 illustrates a Keplerian orbit, with Cartesiancoordinates (x,y) and polar coordinates (r,Ï).

Parametric equations for a general Keplerian orbit are r(Ï) = a(1 â e cosÏ)

t(Ï) = *(T)/2Ï+ ( Ïâ e sinÏ)

tan(Ï/2) = *(1+e)/(1âe)+1/2 tan(Ï/2)

Here Ï is an independent variable. The solution is periodic in Ïwith period âÏ = 2Ï. Also, a, e, T are constants that determine theparameters of the orbit.

Figure 2 shows the relation between Ï and the spatialcoordinates. In the figure, the coordinates (Î¾,Î·) are defined by Î¾= x + ae and Î· = y a /b,

withb=a*1âe2 ]1/2.

(A) What kind of curve is the orbit?

(D) Determine Î¾(Ï) and Î·(Ï).

(E) Express r as a function Ï .

(F) The angular momentum is L = m r2dÏ/dt. Determine L in termsof {a,e,T} Hence verify that L is a constant of the motion.

(G) The energy isE = [1/2] m ( dr/dt )2+ [1/2] m r2(dÏ/dt)2â GMm/r.Determine E in terms of {a,e,T}.

(H) E must be a constant of the motion. Hence determine T and Efrom the equation that you obtained in (F).

(I) Write T in terms of the spatial orbit parameters and theforce constant GM.

(J) Now express L and E in terms of a, e, GM.

(K) In Figure 1, determine the coordinates of the points P, A,and R

(L) In Figure 1, determine the time t at the point R.

PHYSICS 7D Study Guide - Quiz Guide: Electric Field, Electric Potential

PHYSICS 7D Full Course Notes

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