Earth's Magnetic Field and Tangent Law
If Earth's total field makes dip angle delta below horizontal, B_H = B_E cos delta. With a perpendicular horizontal coil field B_c, equilibrium gives tan theta = B_c/B_H.
Why this shows up in the exam
Tangent galvanometer questions · Dip-angle component calculations · Compass deflection and field comparison
Learn the idea
A compass responds to the horizontal component of Earth's field, and a perpendicular coil field obeys the tangent law. The Earth's field is tilted, but a horizontal compass can turn only under its horizontal component. A known transverse field rotates the needle until the two torques balance.
🧠 Memory hook: Horizontal compass sees B cos dip.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- B_H = B_E cos(delta) — horizontal component of Earth's field
- B_V = B_E sin(delta) — vertical component
- tan(theta) = B_c/B_H — tangent law for mutually perpendicular horizontal fields
How to approach it
- 1Resolve Earth's field into horizontal and vertical parts
- 2Draw the added horizontal field
- 3Use vector equilibrium or tan theta = B_c/B_H
Common slip-ups that cost marks
- •Using total Earth field directly in a horizontal compass equation
- •Interchanging sine and cosine of dip
- •Applying tangent law when fields are not perpendicular
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A charge of 2 microC moves perpendicular to a 3 T magnetic field at 4 x 10^5 m/s. Find the magnetic force.
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