a) Calculate the electric field of a point P on the
perpendicular bisector of a dipole. Also calculate the potential
difference from infinity of the point. Also make a sketch of the
equipotential lines and the electric field lines. b) Explain what
happens if we put a large point charge Q at that point P.
If the perpendicular bisector of the line segment joining the points P(1, 4) and Q(k, 3) has y-intercept equal to -4, then a value of k is
(a) 2
(b) -4
(c) 1
(d) -2
The line k goes through the point Q(-3,5) and is perpendicular
to the line g: x - 3y - 22 = 0. Where do the angle bisectors of
lines g and k intersect the line AB when A = (-3,3) and B =
(10,3)?
Write equations of the lines through the given point parallel to
and perpendicular to the given line.
4x + 6y = 0, (7/8,3/4)
(a) parallel to the given line
(b) perpendicular to the given line
Suppose ?⃗ (?,?)=−??⃗ +??⃗ and ? is the line segment from point
?=(2,0) to ?=(0,3).
(a) Find a vector parametric equation ?⃗ (?) for the line
segment ? so that points ? and ? correspond to ?=0 and ?=1,
respectively. ?⃗ (?)=
(b) Using the parametrization in part (a), the line integral of
?⃗ along ? is ∫??⃗ ⋅??⃗ =∫???⃗ (?⃗ (?))⋅?⃗ ′(?)??=∫?? ?? with
limits of integration ?= and ?=
(c) Evaluate the line integral in part (b).
(d)...
Find the equation of the line through the point P = (0,2,−1)
that is perpendicular to both ⃗v = 〈3,0,1〉 and ⃗w = 〈1,−1,2〉.
v and w are vectors by the way
At what radius along the perpendicular bisector of a wire of
length 0.29 m carrying 30 nC of charge does the assumption of
cylindrical symmetry in applying Gauss's law give you an answer
whose error exceeds 5%?
1. write the equations of a line through the point (0, 2, -5)
and perpendicular to the plane -2x+3y+4z = 18. Use either
parametric or symmetric form.
2. Find the acute angle between the planes 2x+4y-z = 12 and
x-6y+5z= 20.
Find parametric equations for the line through the point
(0, 2, 3)
that is perpendicular to the line
x = 2 + t,
y = 2 − t, z
= 2t
and intersects this line. (Use the parameter t.)
(x(t),
y(t),
z(t)) =