Question

A metal disk with a radius of 22 cm rotates with a frequency of 60 rev/s. A magnetic field of 7 T is perpendicular to the disk. A resistor of 70 12 is connected between the center and the edge of the disk. How much current will run through the resistor? Answer in units of A. What torque is required to keep the disk spinning at the same rate? Answer in units of N middot m.

Answer 1

The acceleration of the block after the system is released from rest is 12 m/s².

Step-by-step explanation:

The block is initially at rest and is connected to a spring with a spring constant of 200 N/m. When the system is released, the block will move under the influence of the spring force. The acceleration can be found using Newton's second law:

a = F/m

a = kx/m

a = (200 N/m)(0.1 m)/(5 kg)

a = 12 m/s²

Final Answer:

The current through the resistor is 1.0 A.

Step-by-step explanation:

The disk rotates in a magnetic field, which induces a voltage in the resistor due to electromagnetic induction. The voltage can be found using Faraday's law:

V = NdB/dt

V = (22 cm)(60 rev/s)(7 T)/(2)

V = 14.7 V

The current through the resistor can be found using Ohm's law:

I = V/R

I = 14.7 V/(70 Ω)

I = 0.21 A (rounded to two decimal places)

I = 0.2 A (rounded to one decimal place)

Answer 2

To find the current running through the resistor, we can use Ohm's law and Faraday's law of electromagnetic induction. The current is equal to the voltage divided by the resistance, and the voltage is induced by the magnetic field and the spinning frequency of the disk. To find the torque required to keep the disk spinning at the same rate, we can use the equation for torque, which takes into account the magnetic moment and the magnetic field.

Step-by-step explanation:

To find the current running through the resistor, we can use Ohm's law, which states that the current is equal to the voltage divided by the resistance. In this case, we have a resistor with a resistance of 70 Ω and we need to find the current. The voltage across the resistor can be found using Faraday's law of electromagnetic induction, which states that the voltage induced in a circuit is equal to the rate of change of magnetic flux through the circuit. The magnetic field is given as 7 T and the frequency is given as 60 rev/s. Since the disk has a radius of 22 cm, the magnetic flux through the disk can be calculated as the product of the magnetic field, the area of the disk, and the sine of the angle between the magnetic field and the disk. With this information, we can calculate the current running through the resistor.

To find the torque required to keep the disk spinning at the same rate, we can use the equation for torque, which is given by the product of the magnetic moment, the magnetic field, and the sine of the angle between the magnetic moment and the magnetic field. The magnetic moment of a circular loop with radius R and current I is given by the product of the current, the area of the loop, and the normal vector to the loop. With this information, we can calculate the torque.