Question

If I is the intensity of earth's magnetic field, H its horizontal component and V the vertical component, then these are related as :

• A. $I=V+H$
• B. $I=\sqrt{H^2+V^2}$
• C. $I=\sqrt{H^2-V^2}$
• D. $I=H^2-V^2$

Answer 1

The correct option is B $I=\sqrt{H^2+V^2}$

Intensity of the earth's magnetic field is the vector sum of its horizontal component $H$ and vertical component $V$.

Magnitude of intensity is given by,

$\therefore I=\sqrt{H^2+V^2+2HVcos\theta }$

where $\theta$ is the angle between horizontal and vertical components and it is $\theta ={90}^o$

$\therefore cos\theta =cos{90}^o=0$

$\therefore I=\sqrt{H^2+V^2}$