Multiple-Choice Homework Problem 7.9 The electric potential in a region of space

Question

Multiple-Choice Homework Problem 7.9 The electric potential in a region of space has the form V (r) = r sin(ar), where and a are constants. Calculate the electric field in this region. Select One of the Following:

(a) sin(ar)

(b) + sin(ar)

(c) a cos(ar)

(d) +a cos(ar)

(e) ar cos(ar) sin(ar)

(f) +ar cos(ar) + sin(ar)

Multiple-Choice Homework Problem 7.10 A positively charged particle moves through an electric field. As part of a complicated trajectory, the particle passes through the points A and B. The electric potential of the two points is such that VB > VA. The electric force is the only force acting on the particle. What can be deduced about the speed, v, of the particle at the two points? Select One of the Following:

(a) The speed is equal at the two points.

(b) The speed is larger at A than at B.

(c) The speed is larger at B than at A.

Explanation / Answer

(1)

We know that E=-dv/dr

So E=-(d/dr(r sin(ar)))

=-(sin(ar)+arcos(ar))

=-ysin(ar)-arcos(ar)

Hence option (e) is correct.

(2)

Since Vb>Va

Hence the potential energy of B is greater than A. But bu law of conservation of energy the Potenstial and Kinetic energy sum must be constant. Hence the Kinetic energy of A is greater than B. So A is moving with a greater velocity than A.

So option (b) is correct.

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