Answer:
A) E / B = 2.99 10⁸ V/ mT, B) B = 2.50 10⁻⁶ T
Explanation:
A) the expressions for the energy densities are:
u_E = ½ ε₀ E²
u_B = ½ B² /μ₀
indicate that the two densities are equal
½ ε₀ E² = ½ B² /μ₀
E / B = 1 /[tex]\sqrt{\epsilon_o \ \mu_o }[/tex]
we calculate
E / B = 1 / √( 8.85 10⁻¹² 4π 10⁻⁷
E / B = 1 /√( 11.1212 10⁻¹⁸)
E / B = 0.29986 10⁹9
E / B = 2.99 10⁸ V/ mT
B) for this case E = 750 V / m, ask the magnetic field
E / B = 1 /[tex]\sqrt{\epsilon_o \ \mu_o}[/tex]
B = E [tex]\sqrt{\epsilon_o \ \mu_o}[/tex]
we calculate
B = 750 √(8.85 10⁻¹² 4π 10⁻⁷
B = 750 3.3348 10⁻⁹
B = 2.50 10⁻⁶ T
Energy densities can be expressed as
u_E = ½ ε₀ E²
u_B = ½ B² /μ₀
When the two densities are equal we use the formula
½ ε₀ E² = ½ B² /μ₀
E / B = 1 / μ₀
E / B = 1 / √( 8.85 10⁻¹² 4π 10⁻⁷)
E / B = 1 /√( 11.1212 10⁻¹⁸)
E / B = 0.29986 10⁹
E / B = 2.99 10⁸ V/ mT
E / B = 1 / √ ξ₀ μ₀
B = E √ ξ₀ μ₀
We substitute the values into the equation
B = 750 √(8.85 10⁻¹² 4π 10⁻⁷)
B = 750 3.3348 10⁻⁹
B = 2.50 10⁻⁶ T
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