First slide

Intensity of electromagnetic wave

Question

A long straight wire of resistance R, radius a and length l carries a constant current I. The poynting vector for the wire will be

Moderate

A

$\frac{IR}{2 πal}$
B

$\frac{{IR}^{2}}{al}$
C

$\frac{I^{2} R}{al}$
D

$\frac{I^{2} R}{2 πal}$

Solution

Electric field, $E = \frac{V}{l} = \frac{IR}{l}$ (R = Resistance of wire)
Magnetic field at the surface of wire, $B = \frac{μ_{0} I}{2 πa}$ (a = radius of wire)
Hence, poynting vector, directed radially inward is given by $S = \frac{EB}{μ_{0}} = \frac{IR}{μ_{0} l} \cdot \frac{μ_{0} I}{2 πa} = \frac{I^{2} R}{2 πal}$

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