Which of these expresses the relationship between the earth’s magnetic field FE, and the field’ FB due to a magnet at neutral points? FE is

Analyze the question: A neutral point is a point where the resultant magnetic field is zero. The question asks how the earth's field (FE) relates to the magnet's field (FB) at such a point.

Concept: At a neutral point, the magnetic field of the magnet exactly cancels the horizontal component of the earth's magnetic field. For two fields to cancel and give a zero resultant:

• they must have the same magnitude, and
• they must act in opposite directions.

Solution:

Resultant field at the neutral point = FE + FB = 0

So FE = −FB

This means FE is equal in magnitude to FB and opposite in direction.

Checking the options:

• A. Equal and opposite to FB. This gives a zero resultant, so it is correct.
• B. Same direction would add the fields, not cancel them, so it is wrong.
• C. Same direction and greater would also add them, so it is wrong.
• D. Greater and opposite would leave a net field, so it is not a neutral point.
• E. Less and opposite would also leave a net field, so it is wrong.

Tip: "Neutral = Net zero." If the resultant is zero, the two fields must be equal and opposite. Remember this for questions on neutral points of a bar magnet, whether the magnet's N pole points north (neutral points on the equatorial line) or points south (neutral points on the axial line).