The figure shows four cases involving a changing magnetic field and a loop of wi

Question

The figure shows four cases involving a changing magnetic field and a loop of wire. In all views the lower edge of the loop is closer to the viewer (one is viewing the loops from above the plane of each loop.) The area vectors, shown in the figure, are chosen to point upwards in all cases. The magnetic fields arc also shown in the figure ar.d it is indicated if the field strength is increasing or decreasing. (1) Determine if the fiux is positive or negative in each case. (II) Determine those cases ir. which the fiux is becoming more positive (or less negative) (111) Determine those eases in which the fiux is bccomir.g less positive (or more negative) (IV) Determine the direction of the induced cmf in each case.

Explanation / Answer

Hi,

In order to answer all the questions of this problem we must have in mind the concept of magnetic flux, which is given by the following equation:

F = BA cos (1); where F is the magnetic flux, B is the value of the magnetic field, A is the area over which we are calculating the flux (in this case is the area delimited by the wire) and is the angle between a vector normal to the area and the magnetic field.

(I) In the cases a and b the flux is positive because all the terms in (1) are positive.

In the cases c and d the vector normal to the area and the magnetic field form a angle bigger than 90°, therefore the cos is negative and the value of the flux is negative as well.

(II) The case d is becoming less negative as the value of B is smaller and smaller as time pass by, tending to cero. The case a is similar, as the flux is becoming bigger and bigger with the increase in B, but in the end the flux is not more positive but bigger.

(III) The case c is becoming more and more negative as the value of B increases over time. Something similar happens with the case b , as it tends to cero due to the reduction in the value of B, but it is not less positve, only smaller.

Note: if we consider the real line of number and we consider cero as the reference between positive and negative, then a positive number farther from cero will be more positive than a closer one, and the same can apply to negative numbers. Therefore, we could say that bigger numbers are more positive than others. If that's the case, then we should conclude that b is becoming less positve while a is becoming less negative.

(IV) The induced current in case a and d flows in clockwise sense.

The induced current in case b and c flows in counter clockwise sense.

Note: The direction of the induced current over the wire comes from Lenz's Law, where it is stated that the induced current will flow in the sense that will cause a new magnetic field that will oppose the change in the original magnetic field.

I hope it helps.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

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