Question

The power supplied by a torque t to rotate an object to angular frequency w is p=tw. A common car engine produces t=300 Nm at w=3000 RPM (rotations per minute). Suppose you want to create an electric car that runs on battery and electric motor. Typically, electric car motors utilize a current of 100A and have a cros sectional area of 0.5 m2. Suppose also that the number of wire turns in the coil of the motor is N=100.

Q1. How strong of a magnetic field is required to produce the same torque as a regular car engine?

When the motor is connected in series with the battery that powers it, we can treat it like a generic circuit element with effective resistance R that causes a voltage drop V=IR. By setting the electrical power consumed by the motor equal to the mechanical power used to push the car, P=tw, the effective resistance of the motor can be determined.

Q2. What is the effective resistance of the motor?

Q3. Determine the voltage of the battery.

Answer #1

1) given N = 100

I = 100

A = 0.5

we know that

magnetic moment = NIA = 100*100*0.5 = 5e3

considering the magnetic field is at 90 to the loop i.e. maximum
torque is generated

T = magnetic monent x
B
(cross product)

T = magnetic moment * B * sin(theta)

300 = 5e3 * B * sin(90)

B = **0.06T**

2) we know that

power = T*W

where w is in rad/sec

W = 2pi*3000/60 = 314rad/s

P = 300*314 = 94200

as stated

electrical power consumed = mechanical power

I^2*R = 94200

100^2 * R = 94200

R = 94200/10000 = **9.42ohm**

3)

V = IR = 100*9.42 = **942V**

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