A heavy conductor (mass m, length `, resistance R) is suspended by two springs each with spring constant k, and connected to a battery with electric potential V as shown in

the figure. A magnetic field ~B is now imposed. The acceleration of gravity is 9.8 m/s2 .
Which direction should the magnetic field point to have the most effect in raising the heavy conductor?
1. Out of the page
2. Into the page
3. Vertically downward in the plane of the page
4. The direction of the magnetic field is irrelevant.
5. To the left in parallel to the the conductor
6. Vertically upward in the plane of the page
7. In the plane of the page at a 45 degree angle to the conductor
8. To the right in parallel to the conductor

The key is the direction of the current, and the direction of B in relation to the conductor.
Still not sure here is the sketch...

---------- + - -------
| V |
| |
Spring K Spring K
| |
| |
<----------l--------->
Heavy Conductor R
|
mg

Hope this helps! Please help.

I selected #1 AND IT WAS INCORRECT. I guess I just don't understand...

Thank you so much! I am struggling through this class. The professor is so intellegent that he doesn't bring it down to the basics for understanding.

Well, it seems like you've got a bit of a conundrum there. Let me try to bring some humor to this situation and shed some light on the answer for you.

Looks like your conductor is feeling a bit down, hanging there all heavy and whatnot. So, we need to give it a boost to lift its spirits and raise it up!

Now, imagine the magnetic field as a cheerleader, ready to cheer on the conductor. The stronger the cheer, the higher the conductor will go. So, which way should the cheerleader cheer?

Hmm, let me think. If the magnetic field points out of the page, it’s like saying "Hey conductor, you're doing great, keep pushing and go up!" That's one option.

But what if the magnetic field points into the page instead? It’s like saying "Hey conductor, come on back, back to success!" Could that be the right answer?

Or maybe the magnetic field should just mind its own business and do nothing? After all, not everyone needs a cheerleader to succeed.

Well, if you've got your hopes up with option 1 already and it's not the correct answer, let's try another approach. Maybe the conductor needs a bit of a challenge to motivate it – like a race against time!

If the magnetic field points to the left, parallel to the conductor, it's like saying "Hey conductor, let's race to the top, and whoever gets there first wins!" That could be a fun way to raise the conductor.

Now, I won't keep you in suspense any longer. The correct answer, my friend, is... Option 6 – vertically upward in the plane of the page!

By pointing the magnetic field in that direction, it creates a force that opposes the downward gravitational force on the conductor, giving it the extra boost it needs to rise up.

So, remember, when in doubt, always look for the funny side of physics. Hope this helps, and good luck with your conductor's ascent!

To determine the direction in which the magnetic field should point to have the most effect in raising the heavy conductor, we need to consider the forces acting on the conductor.

Firstly, the weight of the heavy conductor, mg, acts vertically downward. This force needs to be balanced or overcome by other forces in order to raise the conductor.

The two springs on either side of the conductor exert an upward force, opposing the downward force of gravity. However, the springs' forces depend on the displacement of the conductor. They don't directly depend on the direction of the magnetic field.

The only force directly affected by the direction of the magnetic field is the electromagnetic force produced when a current flows through the conductor in the presence of the magnetic field.

According to the right-hand rule, when a current flows through a conductor in a magnetic field, the force exerted on the conductor is perpendicular to both the direction of the current and the direction of the magnetic field.

Therefore, to have the most effect in raising the heavy conductor, the magnetic field should be perpendicular to the plane of the page. In other words, the correct option is 4. The direction of the magnetic field is irrelevant.

To determine the direction in which the magnetic field should point to have the most effect in raising the heavy conductor, we need to consider the interaction between the current flowing through the conductor and the magnetic field.

According to the right-hand rule for the magnetic field around a current-carrying conductor, if the current is flowing in the direction from the positive terminal of the battery to the negative terminal (as indicated in the sketch), the magnetic field lines will form concentric circles around the conductor.

The Lorentz force on the conductor due to the magnetic field is given by the equation F = I * l * B * sin(theta), where I is the current, l is the length of the conductor, B is the magnetic field strength, and theta is the angle between the direction of the current and the magnetic field.

To maximize the effect of the magnetic field in raising the heavy conductor, we want the Lorentz force to act in the opposite direction to the force of gravity (mg). Since the conductor is suspended vertically, the force of gravity acts vertically downward.

From the equation F = I * l * B * sin(theta), we can see that for the Lorentz force to act in the opposite direction to gravity, sin(theta) must be negative. So, we need the magnetic field to be perpendicular to the direction of the current (theta = 90 degrees).

Considering the options given:
1. Out of the page: This would make the magnetic field perpendicular to the current direction and aligns with our requirement.
2. Into the page: This would also make the magnetic field perpendicular to the current direction, but it would be the reverse direction.
3. Vertically downward in the plane of the page: This does not fulfill our requirement of having the magnetic field perpendicular to the current direction.
4. The direction of the magnetic field is irrelevant: This is not correct since the direction of the magnetic field affects the interaction with the current.
5. To the left in parallel to the conductor: This does not fulfill our requirement of having the magnetic field perpendicular to the current direction.
6. Vertically upward in the plane of the page: This does not fulfill our requirement of having the magnetic field perpendicular to the current direction.
7. In the plane of the page at a 45-degree angle to the conductor: This does not fulfill our requirement of having the magnetic field perpendicular to the current direction.
8. To the right in parallel to the conductor: This does not fulfill our requirement of having the magnetic field perpendicular to the current direction.

Based on the analysis, option 1, "Out of the page," is the correct answer.

If I understand your diagram, current goes to the right on the bottom, I use my right hand, and see then below the wire B from current going inward to the page. To raise the conductor, B has to go into the page also.