-A: Find the force that must be exerted on the rod to maintain a constant current of 0.156 A in the resistor? (In mN)

-B: What is the rate of the energy dissipation in the resistor? (In W)

-C: What is the mechanical power delivered to the rod? (In W)

A) Force: 0.0528 N

B) Power dissipated: 0.307 W

C) Power delivered: 0.307 W

Explanation:

A)

The  force experienced by a current-carrying wire in a magnetic field is given by

where

I is the current in the wire

L is the length of the wire

B is the strength of the magnetic field

In this problem, we have:

L = 0.451 m

B = 0.751 T

I = 0.156 A

Therefore, the force is

B)

The rate of energy dissipation in the resistor is the power dissipated in the resistor, and it is given by

where

I is the current in the resistor

R is the resistance

For the wire in this problem,

I = 0.156 A

Therefore, the power dissipated is

C)

The mechanical power delivered to the rod is given by

where

V is the potential difference across the rod

I is the current in the rod

The potential difference across the rod must be equal to the potential difference across the resistance, which can be  found by using Ohm's law:

Therefore, the power delivered to the rod is

This power is equal to the power dissipated on the resistor: this is due to the law of conservation of energy, in fact the total energy must remain constant, so here the electric energy is transformed into mechanical energy of motion of the rod.

a solenoid is created by wrapping a l = 90 m long wire around a hollow tube of diameter d = 4.5 cm.   the wire diameter is d = 0.9 mm.   the solenoid wire is then connected to a power supply so that a current of i = 9 a flows through the wire.

randomized variablesl = 90 m

d = 4.5 cm

d = 0.9 mm

i = 9 a                                          

write an expression for the number of turns, n, in the solenoid. you do not need to take into account the diameter of the wire in this calculation.

calculate the number of turns, n, in the solenoid.

write an expression for the length of the solenoid (l2) in terms of the diameter of the hollow tube d.

calculate the length of the solenoid (l2)   in meters.

calculate the magnitude of the magnetic field at the center of the solenoid in teslas.

explanation:

if they have a finite resultant