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JEE Mains Previous Paper 1 (Held On: 12 Apr 2019 Shift 2)

Option 2 : \(\vec B \) = 2 × 10-7 sin(0.5 × 103 z - 1.5 × 1011t) î

**Concept:**

Electromagnetic waves are changing in electric fields and magnetic fields. Electric field is a charged particle and magnetic field is a moving charged particle.

The magnetic wave in positive z direction is:

\(\vec B = {B_0}\sin \left( {kz - \omega t} \right)\)

The peak magnetic field is given by the formula:

\({B_0} = \frac{{{E_0}}}{c}\)

Where,

E_{0} = Peak value of electric field = 60 V/m

c = Velocity of light = 3 × 10^{8} m/s

**Calculation:**

On substituting values,

\( \Rightarrow {B_0} = \frac{{60}}{{3 \times {{10}^8}}}\)

∴ B_{0 }= 2 × 10^{-7} T

The angular frequency is given by the formula:

ω = 2πf

Where,

f = Frequency of the wave = 23.9 GHz

On substituting values,

⇒ ω = 2π(23.9 × 10^{9})

∴ ω = 1.5 × 10^{11} rad/s

The wave number is given by the formula:

\(k = \frac{\omega }{{{v_p}}}\)

Where,

v_{p} = Phase velocity = 3 × 10^{8} m/s

On substituting values,

\( \Rightarrow k = \frac{{1.5 \times {{10}^{11}}}}{{3 \times {{10}^8}}}\)

∴ k = 0.5 × 10^{-3}

Now, the magnetic wave equation is:

\(\vec B = 2 \times {10^{ - 7}}\sin \left( {0.5 \times {{10}^{ - 3}}z - 1.5 \times {{10}^{11}}t} \right)\hat i\)

Junior Executive (ATC) Official Paper 1: Held on Nov 2018 - Shift 1

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