Prove that I2 - H2 - V2 and tan q - VH- where for terrestrial magnetism - angle of dip- H horizontal component and vertical component-

Let I be the total intensity of earth field, #160; #952; #952; #160;angle of dip horizontal intensity H, vertical intensityAs per figure,Resolving I in ...

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Standard XII

Physics

Magnetic Dip

Prove that I...

Question

Prove that
$I^{2} = H^{2} + V^{2}$ and $t a n q = \frac{V}{H}$ ; where for terrestrial magnetism $θ$ angle of dip, H horizontal component and vertical component.

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Solution

Let I be the total intensity of earth field, θ angle of dip horizontal intensity H, vertical intensity
As per figure,
Resolving I in two ⊥ directions, we get
Horizontal component H = I cos θ .......... (i)
Vertical component V = I sin θ ......... (ii)
(ii) ÷ (i) $V H = I s i n θ I c o s θ$
$t a n θ = V H$
Also by squaring and adding equations (1) and (2),
$I^{2} c o s^{2} θ + I^{2} s i n^{2} θ = H^{2} + V^{2}$
$I^{2} = H^{2} + V^{2}$

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Prove thatI2=H2+V2 and tanq=VH; where for terrestrial magnetism θ angle of dip, H horizontal component and vertical component.

Prove that
$I^{2} = H^{2} + V^{2}$ and $t a n q = \frac{V}{H}$ ; where for terrestrial magnetism $θ$ angle of dip, H horizontal component and vertical component.