- #1

- 91

- 1

A metal bar of mass m slides frictionlessly on two conducting rails a distance l apart as shown in the attached Figure 1. A resistor R is connected across the rails and a uniform magnetic field B, directed into the page fills the entire region.

a) If the bar is moving to the right at speed v, what is the current flowing through the resistor?

b) In what direction is the current flowing?

c) Calculate the magnetic force acting on the moving bar.

d) What is the direction of the magnetic force acting on the moving bar?

e) If the bar is given an initial speed v0 at time t = 0 directed towards the right, and is thereafter left to slide on its own, derive an expression for the speed of the bar at time t > 0.

f) The initial kinetic energy of the bar was 1/2mvo^2. If the bar is alllowed to slide until it comes to a stop, show that the energy dissipated in the resistor is 1/2mv0^2.

I don' t know if the picture is goina come out right...there is a large rectangular loop with a resistor along the left side of it in the center. The right side is removed and somewhere along , there is a bar parallel to the left side that is being moved.

||

|---------------||---------------------------

| ||

| ||

| ||

R || <----- bar of mass m

| ||

| ||

| ||

|---------------||--------------------------

||

the flux through the resistor is increasing as the bar is moved to the right. This means that there should be an emf that causes a magnetic field that has to oppose the change in flux. This induced B field should be pointing out of the page. This should mean that the current is flowing counter clockwise. I am not sure how to calculate this current.

For the magnetic force I know that it is supposed to be some kinda integral but not sure what.... For its direction, well would this direction be dependent on the result of the integral.. I mean after choosing a path and getting a non zero result, if the result is negative then the path has to be traversed in the opposite direction and then the direction is easily seen by just flipping the direction.

Now, for 3 and f, I am really lost. I have not seen any speed or energy derivation related to this kind of thing in the text so I am really confused as to what I would be comparing it to...I think it might be something like E before = E after but do not know the elements.

Any assistance would be great..thanks!

a) If the bar is moving to the right at speed v, what is the current flowing through the resistor?

b) In what direction is the current flowing?

c) Calculate the magnetic force acting on the moving bar.

d) What is the direction of the magnetic force acting on the moving bar?

e) If the bar is given an initial speed v0 at time t = 0 directed towards the right, and is thereafter left to slide on its own, derive an expression for the speed of the bar at time t > 0.

f) The initial kinetic energy of the bar was 1/2mvo^2. If the bar is alllowed to slide until it comes to a stop, show that the energy dissipated in the resistor is 1/2mv0^2.

I don' t know if the picture is goina come out right...there is a large rectangular loop with a resistor along the left side of it in the center. The right side is removed and somewhere along , there is a bar parallel to the left side that is being moved.

||

|---------------||---------------------------

| ||

| ||

| ||

R || <----- bar of mass m

| ||

| ||

| ||

|---------------||--------------------------

||

the flux through the resistor is increasing as the bar is moved to the right. This means that there should be an emf that causes a magnetic field that has to oppose the change in flux. This induced B field should be pointing out of the page. This should mean that the current is flowing counter clockwise. I am not sure how to calculate this current.

For the magnetic force I know that it is supposed to be some kinda integral but not sure what.... For its direction, well would this direction be dependent on the result of the integral.. I mean after choosing a path and getting a non zero result, if the result is negative then the path has to be traversed in the opposite direction and then the direction is easily seen by just flipping the direction.

Now, for 3 and f, I am really lost. I have not seen any speed or energy derivation related to this kind of thing in the text so I am really confused as to what I would be comparing it to...I think it might be something like E before = E after but do not know the elements.

Any assistance would be great..thanks!

Last edited: