1.) (10pts total ) i) An infinitely long solenoid (radius a, centered on the z-a
ID: 1580319 • Letter: 1
Question
1.) (10pts total ) i) An infinitely long solenoid (radius a, centered on the z-axis) carries a current which is counterclockwise (as viewed from the +z axis) and has been steadily (linearly) increasing for a long time (from well beforet -0 to long after.) There are no other charges or currents anywhere nearby What can you say about the electrie field at a point P on the ty axis, located at y=2a (outside the solenoid) at t-0? A) It is zero. B) It points in the +x direction. C) It points in the -x direction D) It points in the ty direction E) It points in the -y direction F) It points in the +z direction G) It points in the -z direction H) Something else, it's none of the above! a 2a ii) Next, consider a small imaginary loop centered on point P, sitting in the x-y plane, with radius a/5. (So, this loop is a little ring around point P, located entirely outside the solenoid) If you integrate E dl around that loop, ccW (counterclockwise as viewed from the positive z axis) what is the sign of the integral? A) Positive D) Not enough information to decide. B) Negative C) Zero ii) Now consider a different imaginary loop, again sitting in the x-y plane, now centered on the origin, with radius 2a. (So, this loop runs through the point P, circling the solenoid nicely, on the ouside If you integrate fB-dl around that loop, CCW (counterclockwise) as viewed from the positive z axis, what is the sign of this integral? (Please note: we are integrating B now, not E!) B) Negative C) Zero D) Not enough infomaton to decide D) Not enough information to decide.Explanation / Answer
a)
Electric field at that point muist be zero
as it lies out of the loop
b)
Its sign is negative as the field due to solenoid is opposite the plane of loop
c)
ZERO
as the enclosed current in the loop is zero
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