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
without a drawing or sketch, this cannot be answered. The key is the direction of the current, and the direction of B in relation to the conductor.
---------- + - -------
| V |
| |
Spring K Spring K
| |
| |
<------------l------------>
Heavy Conductor R
|
mg
Hope this helps! Please help.
To determine the direction of the magnetic field that will have the most effect in raising the heavy conductor, we need to apply the right-hand rule for magnetic fields. Here's how we can do that:
1. Hold your right hand flat and point your thumb in the direction of the current flow in the conductor. In this case, the current is flowing from the battery towards the bottom of the conductor.
2. Curl the fingers of your right hand. The direction in which your fingers curl represents the direction of the magnetic field created by the current flowing in the conductor.
3. Now, let's consider each of the given options and see which one matches the direction of the magnetic field that we found using the right-hand rule:
a. Out of the page: If the magnetic field is pointing out of the page, it means the magnetic field lines are perpendicular to the plane of the page. This option does not match the direction we found using the right-hand rule.
b. Into the page: If the magnetic field is pointing into the page, it means the magnetic field lines are perpendicular to the plane of the page in the opposite direction. This option does not match the direction we found using the right-hand rule.
c. Vertically downward in the plane of the page: If the magnetic field is pointing vertically downward in the plane of the page, it means the magnetic field lines are parallel to the conductor. This option does not match the direction we found using the right-hand rule.
d. The direction of the magnetic field is irrelevant: This option implies that the magnetic field does not have any effect on the heavy conductor, which is incorrect. The magnetic field will indeed have some effect on the conductor due to electromagnetic interactions.
e. To the left in parallel to the conductor: If the magnetic field is pointing to the left in parallel to the conductor, it means the magnetic field lines are perpendicular to the path of current flow in the conductor. This option matches the direction we found using the right-hand rule.
f. Vertically upward in the plane of the page: If the magnetic field is pointing vertically upward in the plane of the page, it means the magnetic field lines are parallel to the conductor. This option does not match the direction we found using the right-hand rule.
g. In the plane of the page at a 45-degree angle to the conductor: If the magnetic field is pointing in the plane of the page at a 45-degree angle to the conductor, it means the magnetic field lines are not perpendicular or parallel to the conductor. This option does not match the direction we found using the right-hand rule.
h. To the right in parallel to the conductor: If the magnetic field is pointing to the right in parallel to the conductor, it means the magnetic field lines are perpendicular to the path of current flow in the conductor. This option matches the direction we found using the right-hand rule.
Therefore, the correct answer is option 5. The magnetic field should point to the left in parallel to the conductor to have the most effect in raising the heavy conductor.