A copper wire loop is constructed so that its radius, r. can change. It is held

Question

A copper wire loop is constructed so that its radius, r. can change. It is held near a solenoid that has a constant current through it. Suppose that the radius of the loop were increasing Use Lenz's law to explain why there would be an induced current through the wire. Determine the direction of the induced current in two ways. In each case, explain your reasoning: using Lenz's law considering the magnetic force that is exerted on the charge in the wire of the loop Determine the direction of the magnetic moment of the loop. Explain. Determine the direction of the force exerted on the loop by the solenoid. Explain. A copper wire loop is initially at rest in a uniform magnetic field. Between times t = t1 and t = t1 + Delta t the loop is rotated about a vertical axis as shown. Will current flow through the wire of the loop during this time interval? If so. indicate the direction of the induced current and explain your reasoning. If not, explain why not.

Explanation / Answer

1
a) its already been done by you

b)
Lenz's Law:
Looking from the left side perpendicularly to the plane of the loop,
as the area of loop increases, the flux in the cross direction is increasing and according to lenz's law, a current will be induced which opposes this change in flux, that is a current will be produced such that it produces a flux in the dot direction
Hence, a counter-clockwise current will be induced (don't forget as looking from left side )


Magnetic Force:
Again Looking from the left side perpendicularly to the plane of the loop,
let us consider an electron residing in the topmost point of the loop.
Now, as the radius is increased, this electron is also shifting upwards along with it.
which implies it has some velocity in the upward direction(say j(cap))
the magnetic field is in the cross direction(say -k(cap))
Now, the lorentz force acts on this particle given by : F = q(v(vector) x B(vector))

so the direction of F will be : -1*(j(cap) x -k(cap)) = j(cap) x k(cap) = i(cap)
( -1 accounts for the negative charge of electron)

i(cap) => force on electron is in right direction which will lead to a clockwise motion in the loop.
Now, since electrons are negatively charged the direction of current is opposite to their direction of motion.
Therefore, current flows in counter-clockwise direction (don't forget as looking from left side )


c) Magnetic Moment
direction of magnetic moment is given by right hand thumb rube where
curl of fingers => direction of current
thumb => direction of magnetic moment

in our case
direction of current => counter-clockwise
then ,
magnetic moment = > dot direction ( as seen from left)
=> towards left ( as in the given diagram)

d)as loop has an induced current that opposes the direction of magnetic field produced by solenoid, so in order to reduce its effect, a force is exerted on the loop that pushes it away from the solenoid
=> direction of force is left (as seen in given diagram )

2.

as the loop rotates , the projection of the area of loop in the direction perpendicular to that of the magnetic field is decreasing and in the end it becomes zero

it is this projection of area that is used in the formula (B*A) of flux

=> flux is decreasing

=> a currect will be induced to counter it( Lenz's Law )

=>as seen from the left, flx is in cross direction, and decreasing

=> current produced in clockwise direction

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.