Force on a Current Carrying Conductor

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The discussion centers on determining which scenarios result in a magnetic force on a current-carrying wire pointing due north. The right-hand rule is referenced to analyze the interactions between current direction and magnetic field orientation. The participant identifies the third scenario as correct but is uncertain about additional correct answers. They conclude that when the current flows up with an eastward magnetic field, the resulting force is north, and reversing both current and field also yields a northward force. The conversation emphasizes the application of magnetic force principles to various configurations of current and magnetic fields.
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Homework Statement



Which of the following situations would result in a magnetic force on the wire that points due north?

Check all that apply.

Current in the wire flows straight down; the magnetic field points due west.
Current in the wire flows straight up; the magnetic field points due east.
Current in the wire flows due east; the magnetic field points straight down.
Current in the wire flows due west and slightly up; the magnetic field points due east.
Current in the wire flows due west and slightly down; the magnetic field points straight down.

Homework Equations



Right hand rule of left hand rule

The Attempt at a Solution



I know that the third one is correct but it says that the answer is wrong which means there is atleast one other correct answer but I have NO CLUE which one that is. Please help.
 
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A. When the current is up and the magnetic field is East, the force is North.
B. When both current and field in A are reversed, the force is North.
If the current is mostly West and slightly up you have situation A but a weaker force to the North.
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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