JEE Mains · Physics · STD 12 - Electromagnetic waves
- JEE Mains 2026
- Hard
- MCQ
The electric field a plane electromagnetic wave is given by :
\(E _y=69 \sin \left[0.6 \times 10^3 x -1.8 \times 10^{11} t \right] V / m\).
The expression for magnetic field associated with this electromagnetic wave is _________ T.
Pick an option to check your answer.
Answer & Solution
Correct Answer
(A) \( B_{z} = 2.3 \times 10^{-7} \sin[0.6 \times 10^{3}x - 1.8 \times 10^{11}t] \)
Step-by-step Solution
Detailed explanation
\(\hat{ B }=\hat{ c } \times \hat{ E }\)
\(\Rightarrow \quad \hat{ c }=\hat{ i }\) because phase of electric field is function of \(x\).
\(\Rightarrow \quad \hat{ E }=\hat{ j }\) (given)
\(\Rightarrow \quad \hat{ B }=\hat{ i } \times \hat{ j }=\hat{ k }\)
\(| B |=\frac{| E |}{ c }=\frac{69 \times 0.6 \times 10^3}{1.8 \times 10^{11}}=\frac{69}{3 \times 10^8}\)
\(| B |=2.9 \times 10^{-7}\)
\(\overrightarrow{ B }_2=2.9 \times 10^{-j} \sin \left(0.6 \times 10^3 x -1.8 \times 10^{11} t \right)\)
(phase is same as that of electric field)
\(\Rightarrow \quad \hat{ c }=\hat{ i }\) because phase of electric field is function of \(x\).
\(\Rightarrow \quad \hat{ E }=\hat{ j }\) (given)
\(\Rightarrow \quad \hat{ B }=\hat{ i } \times \hat{ j }=\hat{ k }\)
\(| B |=\frac{| E |}{ c }=\frac{69 \times 0.6 \times 10^3}{1.8 \times 10^{11}}=\frac{69}{3 \times 10^8}\)
\(| B |=2.9 \times 10^{-7}\)
\(\overrightarrow{ B }_2=2.9 \times 10^{-j} \sin \left(0.6 \times 10^3 x -1.8 \times 10^{11} t \right)\)
(phase is same as that of electric field)
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