The metal has free electrons which move through the magnetic field along with the metal. These are charges moving through a magnetic field. They feel a force acting on them

Using the right hand rule, it can be shown that the electrons will move to the top of the bar, leaving the bottom with a net positive charge. Now there is an electric field between the top and bottom of the metal bar. There is an electric force acting on the particles in the bar,

where  is the electric field. The electric force will now be equal and opposite the magnetic force so the charges will settle and not continue to move out of the bar. Setting these forces equal, the charge will divide out.

The electric field is just the motional emf per unit length,

Solving for v,

In this question, we're presented with a scenario in which an electron is traveling east in a magnetic field that is pointing away from the viewer. We're asked to determine the direction in which the magnetic force on this electron points.

To answer this question, we'll need to use the "right-hand rule." This is a useful trick that allows us to relate the relative orientations of three quantities:

1) The velocity of a positively charged particle moving in a magnetic field

2) The direction of the magnetic field

3) The magnetic force experienced by the moving particle

In addition, there is an equation that relates these three quantities:

In such a situation, all three of the above quantities are oriented perpendicularly to each other. The right-hand rule is a useful way of remembering how each term is oriented with respect to each other. Using the right hand, the thumb represents the direction of the particle's velocity. The index finger represents the direction of the external magnetic field. And lastly, the direction that the palm is facing is the same as the direction of the magnetic force that is acting on the moving particle.

Keep in mind that these orientation are true for a positively charged particle. In order to determine the relative orientations of these terms for a negative particle, simply reverse the direction of the force.

In this problem, the particle is traveling east (to the right) and the magnetic field is pointing outwards, away from the viewer. Therefore, if we use our right hand and point our thumb towards the right and our index finger away from us, our palm is facing up. But since this is a negatively charged electron, we'll need to reverse the direction of the force. Hence, instead of pointing up (north) the force is pointing down (south).

Use the right hand rule. The first vector, the velocity is represented by the thumb pointing to the west. The resultant vector, the middle finger (or palm) is pointed to the sky. The index finger is pointed south.

Using the right hand rule for magnetic fields, it is seen that the magnetic field is point into the page at location . Using the right hand rule for force on a moving positively charged particle, it is seen that the force is acting down.

From the right hand rule for a current carrying wire, the magnetic field is pointing into the page. From the right hand rule for magnetic force, the force is pointed down on a negatively charged electron.

Per conventional symbols, the "X" represents electrons traveling into the page, and the "dot" represents electrons coming out of the page. Picking either electron and using the right hand rule for current traveling, then reversing for the negative charge of the electron gives us the direction of the magnetic field at the other electron. Using the right hand rule again for moving charges in a magnetic field, then reversing for the negative charge of the electron shows that the charges will experience an attractive magnetic force.

In this question, we're shown the path an electron takes as it moves outward in a counter-clockwise direction. We're asked to find the correct orientation of the magnetic field that will cause the electron to move this way.

There are a couple of things to note in this question. First, we know that the electron is traveling in a circular motion. This is true even though it is accelerating outwards. Thus, it must be experiencing some form of centripetal force to stay in its partially circular path.

Also, the source of that centripetal force must be the magnetic field. We know that it cannot be contributed by gravity, as the charge of an electron makes its gravitational mass insignificant.

Since the magnetic force is the source of the centripetal force, we can use this to determine how the magnetic field needs to be oriented. To do this, we use the right-hand rule. Although there is more than one way to use this rule, we can use one of them; the thumb points in the direction of the moving charge, the rest of the fingers point in the direction of the magnetic field, and the palm faces in the direction of the magnetic force vector. And remember, this only works with the right hand!

If we use our thumb to represent the motion of the electron, our fingers will point forward (pointing into the page). Moreover, our palm will always be facing towards the center of the circle. This is what we're looking for. This represents a situation where the magnetic force acts as the centripetal force by always pointing toward the center of the circular path of the electron.

And last but certainly not least, one crucial thing to remember is that we are following a negative charge! The right hand rule is meant to work for positive charges. To correct this, we can reverse the orientation of the magnetic field that we found. Originally, our fingers pointed into the page, suggesting that the magnetic field vector would point into the page. If we reverse this, then the magnetic field vector would point out of the page. Thus, the correct answer is that the magnetic field would need to be pointing out of the page in order to keep the electron moving in its partially circular path.

Write the formula for induced electromotive force.

Since there are two loops, .

Solve for .

Current is induced in wire when the magnetic flux changes. When the magnetic rod is in motion, the flux is changing, so current is induced. If the coil were expanded or contracted with the rod still there, the flux would change and current would be induced. In our case, the rod is stationary and the coil isn't changing shape. Therefore, the flux is not changing, so there is no current being induced. Additionally, there's no reason for the rod to lose its magnetic property.

When a conductor moves through a magnetic field in such a way that it cuts through magnetic field lines, the mobile charge carriers separate due to the magnetic force on them, creating a potential . Since there is no resistance anywhere else in the circuit, all of this potential is lost in the resistor, so we can apply Ohm's law:

Because the positive charge in the rod feels an upward force due to the right-hand rule, the top of the rod has a greater potential than the bottom, and current flows counterclockwise around the circuit, resulting in a downward direction in the resistor.