Question

At a place , the horizontal and vertical components of the earth's magnetic field are $0.4\times {10}^{-4}\text{T}\text{and}0.3\times {10}^{-4}\text{T}$ respectively. The resultant earth's magnetic field will be

• A. $2\times {10}^{-4}\text{T}$
• B. ${10}^{-4}\text{T}$
• C. $0.5\times {10}^{-4}\text{T}$
• D. $0.8\times {10}^{-4}\text{T}$

Answer 1

The correct option is C $0.5\times {10}^{-4}\text{T}$

Resultant of earth's magnetic field , $B=\sqrt{B_H^2+B_V^2}$

Substituting the data given in the question gives,

$B=\sqrt{\left[\right(0.4{)}^2+\left(0.3{)}^2\right]\times {10}^{-8}}$

$\Rightarrow B={10}^{-4}\times \sqrt{0.16+0.09}=\sqrt{0.25}\times {10}^{-4}=0.5\times {10}^{-4}\text{T}$

Hence, option (c) is the correct answer.