Using a coil made of 117 turns of single-strand copper wire, you use a motor to rotate the coil at a constant angular speed of 30.0 revolutions per second at various orientations and locations throughout the room. In one particularly significant orientation, you notice a maximum induced voltage of 2.15 V appearing in the coil. If the radius of the coils is 1.00 cm, how strong was the magnetic field that produced this EMF?

Question

Using a coil made of 117 turns of single-strand copper wire, you use a motor to rotate the coil at a constant angular speed of 30.0 revolutions per second at various orientations and locations throughout the room. In one particularly significant orientation, you notice a maximum induced voltage of 2.15 V appearing in the coil. If the radius of the coils is 1.00 cm, how strong was the magnetic field that produced this EMF?

I have tried using the EMF=NBAwsin(wt) to solve for B, and inputting the numbers for the variables is okay, but I can't figure out how to solve for time in order to multiply it by omega. so I have 2.15=117*B*(.01^2 x pi)*30*sin(30t)

Answer 1

To solve for the magnetic field strength (B), we need to rearrange the equation and solve it step by step. Let's go through the process:

Given:
Number of turns (N) = 117
Radius of the coil (r) = 1.00 cm = 0.01 m
Angular speed (ω) = 30.0 revolutions per second = 30.0 × 2π radians per second (since there are 2π radians in one revolution)

The equation for the induced electromotive force (EMF) in a coil is:
EMF = NBAωsin(ωt)

We're given that the maximum induced voltage (EMF) is 2.15 V, so we can write:
2.15 V = 117 × B × π × (0.01 m)² × (30.0 × 2π) × sin(ωt)

Now, let's analyze the equation and solve for the magnetic field strength (B):

Step 1: Simplify the equation

2.15 V = 117 × B × π × (0.01 m)² × 180π × sin(ωt) [Note: I replaced 30.0 × 2π with 180π]

Step 2: Rearrange the equation

B = (2.15 V) / (117 × π × (0.01 m)² × 180π × sin(ωt))

Step 3: Substitute appropriate values

B = (2.15 V) / (117 × π × 0.0001 m² × 180π × sin(ωt))

Now, you have the equation to calculate the magnetic field strength (B). To find the value of B, you need to know the value of sin(ωt). Unfortunately, without additional information about the specific time (t) and orientation, we cannot calculate the magnetic field precisely.

Therefore, you need to measure the value of sin(ωt) for the particular orientation where the maximum induced voltage was observed at a known time (t). Once you have the value of sin(ωt), you can substitute it into the equation to calculate B.