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To calculate the energy density (energy per unit volume) in an electric field, we can use the formula:
[ u = frac{1}{2} varepsilon E^2 ]
where ( u ) is the energy density in joules per cubic meter (J/m^3), ( varepsilon ) is the permittivity of the material in farads per meter (F/m), and ( E ) is the electric field intensity in volts per meter (V/m).
Given:
– Permittivity, ( varepsilon = 56 , text{F/m} ) (since the units aren’t specified and your question involves basic electromagnetic theory, I’m assuming the permittivity is given in the standard SI unit of farads per meter,).
– Electric field intensity, ( E = 36pi , text{V/m} ) (again assuming the standard SI unit for E since the question doesn’t specify).
Substitute these values into the formula:
[ u = frac{1}{2} times 56 times (36pi)^2 ]
[ u = 28 times 1296pi^2 ]
[ u = 36288pi^2 , text{J/m}^3 ]
Where ( pi^2 approx 9.8696 ), we have:
[ u approx 36288 times
Answer: a
Explanation: The energy in an electric field is given by, W = 0.5 x D x E. Since D = εE,
we get W = 0.5 x ε x E2. On substituting the data, we get 3.16 microjoule.