Question

The total intensity of the earth's magnetic field at the magnetic equator is 5 units.What is its value a magnetic latitude of 37 degree?

• A. $\sqrt{73}$ units
• B. $\sqrt{53}$ units
• C. 4 units
• D. 3 units

Answer 1

Answer: (B)

$\sqrt{53}$ units

$Given:$ Earth's magnetic field = 5 units

$Solution:$ If we are assuming earth as adipole of moment $M$

then magnetic field at any point at distance $d$ and angle $\theta$ from axis of dipole ( means line joining poles)

So, magnetic field = $\frac{\mu o}{4\pi }$ $\frac{M}{d^3}$ $\sqrt{1+3{\cos }^2\left(\theta \right)}$

So at eqator $Beq$ = $\frac{\mu o}{4\pi }$ $\frac{M}{d^3}$ = $5$$unit$ ($\theta$ =90)

and at latitude 37

and angle $\theta$ = 90- 37 = 53

so magnetic field at this point = $\frac{\mu o}{4\pi }$ $\frac{M}{d^3}$ $\sqrt{1+3{\cos }^2\left(53\right)}$ = $5$ $\frac{\sqrt{53}}{5}$

= $\sqrt{53}$ $unit$