A horizontal straight wire of length L extending from east to west is falling with speed v at right angles to the horizontal component of Earth's magnetic field B. (i) Write the expression for the instantaneous value of the e.m.f. induced in the wire. (ii) What is the direction of the e.m.f. ? (iii) Which end of the wire is at the higher potential ?

When a horizontal wire falls through a magnetic field, it experiences electromagnetic induction, which leads to the generation of an electromotive force (e.m.f.). Let's break down your question step by step.

Instantaneous Value of the Induced e.m.f.

According to Faraday's law of electromagnetic induction, the induced e.m.f. (ε) can be expressed using the formula:

ε = B * L * v

Here:

• B is the magnetic field strength (measured in teslas),
• L is the length of the wire (in meters), and
• v is the speed of the wire (in meters per second).

This equation indicates that the induced e.m.f. is directly proportional to the magnetic field strength, the length of the wire, and the speed at which the wire is moving through the magnetic field.

Determining the Direction of the Induced e.m.f.

To find the direction of the induced e.m.f., we can use the right-hand rule. Point your thumb in the direction of the velocity of the wire (downward, in this case, since it is falling), and your fingers in the direction of the magnetic field (which typically points from north to south). The palm of your hand will then indicate the direction of the induced current, which corresponds to the direction of the e.m.f.

Identifying the Higher Potential End

Once we establish the direction of the induced current, we can determine which end of the wire is at a higher potential. If the current flows from east to west, then the eastern end of the wire is at a higher potential compared to the western end.

In summary:

• The induced e.m.f. can be calculated using the formula ε = B * L * v.
• The direction of the induced e.m.f. can be determined using the right-hand rule, leading to the current flowing from east to west.
• The eastern end of the wire is at a higher potential than the western end.

This understanding of electromagnetic induction is fundamental to many applications, including electric generators and motors. If you have any further queries or need clarification on any point, feel free to ask!