To determine the current required to generate 3 Nm of torque in the motor, we'll need to use the formula for the torque produced by a current-carrying coil in a magnetic field. The formula for the torque ($\tau$) is given by:

$\tau = n B I A$

where:

• $n$ is the number of turns in the coil
• $B$ is the magnetic flux density
• $I$ is the current
• $A$ is the area of the coil

Given the following dataTo determine the current required to generate 3 Nm of torque in the motor, we'll need to use the formula for the torque produced by a current-carrying coil in a magnetic field. The formula for the torque ($\tau$) is given by:

$\tau = n B I A$

where:

• $n$ is the number of turns in the coil
• $B$ is the magnetic flux density
• $I$ is the current
• $A$ is the area of the coil

Given the following

• Number of turns ($n$) = 190
• Magnetic flux density ($B$) = 1450 mT = 1450 \times 10^{-3} T = 1.45 T
• Required torque ($\tau$) = 3 Nm
• Coil radius ($r$) = 30 cm = 0.30 m
• Effective length of the coil ($l$) = 22 cm = 0.22 m

The area of the coil ($A$) can be calculated using the formula for the area of a rectangle (since the effective length and coil radius define the rectangular area): $A = 2 \times r \times l$ since both sides of the coil will interact with the magnet.

Substituting the values: $A = 2 \times 0.30 \, \text{m} \times 0.22 \, \text{m} = 0.132 \, \text{m}^2$

Now, using the torque formula, we solve for the current ($I$): $I = \frac{\tau}{n B A}$

Substituting the given values: $I = \frac{3 \, \text{Nm}}{190 \times 1.45 \, \text{T} \times 0.132 \, \text{m}^2}$

$I = \frac{3}{190 \times 1.45 \times 0.132}$

$I = \frac{3}{36.438}$

$I \approx 0.0823 \, \text{A} = 82.32 \, \text{mA}$

Therefore, the current required to generate 3 Nm of torque is approximately 82.32 mA.

Would you like any more details or have any questions about this calculation? Here are five more questions you might ask:

1. How does changing the number of turns in the coil affect the required current?
2. What is the significance of the magnetic flux density in this problem?
3. How would the required current change if the coil radius were different?
4. Can you explain the relationship between torque and the area of the coil?
5. What other factors could influence the torque generated in this motor?

Tip: Always ensure that all units are consistent when performing calculations to avoid errors.