A rectangular coil of wire has a dimensions of 4.9 cm by 9.7 cm and is wound with 84 turns of wire. It is turned between the pole faces of a horseshoe magnet that produces an approximately uniform field of 0.54T, so that sometimes the plane of the coil is perpendicular to the field and sometimes it is parallel to the field.

Question

A rectangular coil of wire has a dimensions of 4.9 cm by 9.7 cm and is wound with 84 turns of wire. It is turned between the pole faces of a horseshoe magnet that produces an approximately uniform field of 0.54T, so that sometimes the plane of the coil is perpendicular to the field and sometimes it is parallel to the field.

Part A: What is the area bounded by the rectangular coil? Answer: 0.004753 m^2

Part B: What is the maximum value of the total magnetic flux that passes through the coil as it is turned? Answer: 0.215628 T*m^2

Part C: If the coil makes on complete turn each 0.5s and turns at a uniform rate, what is the time involved in changing the flux from the maximum value to the minimum value? Answer is in seconds.

Here's where I get lost I thought the answer was 42 s, but that wasn't correct, then maybe thought 84 s was the answer still wrong.

Answer 1

To find the time involved in changing the flux from the maximum value to the minimum value, we need to determine the angular velocity of the coil.

The coil makes one complete turn each 0.5s, which means it completes 1 revolution in 0.5s.

Since the coil has 84 turns, it completes 84 revolutions in 0.5s.

To find the angular velocity (ω), we use the formula:

ω = 2πf

Where:
ω is the angular velocity,
π is a mathematical constant approximately equal to 3.14159, and
f is the frequency in hertz.

In this case, the frequency (f) is the reciprocal of the time taken for one revolution, which is 1/0.5 = 2 Hz.

Substituting the values into the formula, we have:

ω = 2π(2) = 4π rad/s

Now, we know that the time taken to complete one full revolution is given by:

T = 2π/ω

Substituting the value of ω, we have:

T = 2π/(4π) = 0.5s

This means that it takes 0.5 seconds to complete one full revolution.

However, the question asks for the time involved in changing the flux from the maximum value to the minimum value, which is half of the time taken for one full revolution.

Thus, the correct answer is:

0.5s / 2 = 0.25s

Therefore, the time involved in changing the flux from the maximum value to the minimum value is 0.25 seconds.