Consider two single turn coils labeled 1 and 2 that are positioned close to each other. The switch S has been open for a long time. If the switch is now closed and the current through coil 1 is in the direction shown and increasing, which of the following statements is true?
a.The current in coil 2 will be in the same direction as in coil 1.
b.The current in coil 2 will be in the opposite direction as in coil 1.
c. There will be no current in coil 2.
d.The direction of the current in coil 2 will depend on the size of the resistance R.
e. The direction of the current in coil 2 will depend on whether the area of coil 2 is larger or smaller than that of coil 1.
The correct answer is c. There will be no current in coil 2.
Explanation:
When the switch is closed, an electric current is induced in coil 1 due to the changing magnetic field. This changing magnetic field induces an electromotive force (emf) according to Faraday's Law of electromagnetic induction. This emf causes an electric current to flow in coil 1.
Since the switch has been open for a long time, there is no pre-existing magnetic field surrounding coil 2. Therefore, there is no changing magnetic field to induce an emf in coil 2. As a result, no electric current is generated in coil 2.
To determine the direction of the current in coil 2 when the switch is closed and the current through coil 1 is increasing, we need to apply Faraday's law of electromagnetic induction. According to this law, a changing magnetic field induces an electromotive force (EMF) in a nearby conductor, which causes a current to flow.
In this scenario, when the current through coil 1 is increasing, it produces a magnetic field. This changing magnetic field induces an EMF in coil 2 and generates a current.
Now, let's evaluate the options to determine which statement is true:
a. The current in coil 2 will be in the same direction as in coil 1.
This option is possible since a changing current in coil 1 generates a changing magnetic field, which induces a current in coil 2 in the same direction.
b. The current in coil 2 will be in the opposite direction as in coil 1.
This option is also possible since a changing current in coil 1 generates a changing magnetic field, which induces a current in coil 2 in the opposite direction.
c. There will be no current in coil 2.
This option is not correct. Faraday's law states that a changing magnetic field induces an EMF, which in turn causes a current to flow in a nearby conductor.
d. The direction of the current in coil 2 will depend on the size of the resistance R.
This option is incorrect because the size of the resistance R does not affect the direction of the induced current. It only affects the magnitude of the current.
e. The direction of the current in coil 2 will depend on whether the area of coil 2 is larger or smaller than that of coil 1.
This option is also incorrect. The direction of the induced current in coil 2 depends on the changing magnetic field caused by the increasing current in coil 1. The relative areas of the coils do not influence the direction of the induced current.
In conclusion, both options a and b are possible. The direction of the current in coil 2 will depend on the specific conditions, such as the orientation and proximity of the coils. To determine the direction with certainty, further information about the specific setup is required.