NCERT Physics Class 12 Exemplar Ch 8 Electromagnetic Waves Part 5

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Q 31 A plane EM wave travelling in vacuum along z direction is given by .

(i) Evaluate. Over the rectangular loop shown in Figure.

(ii) Evaluate. Over the surface bounded by loop 1234.

(iii) Use equation to prove

(iv) By using similar process and the equation

Evaluate flux rectangular loop 1234 (Q)

Evaluate Flux Rectangular Loop 1234 (Q)

Evaluate flux rectangular loop 1234 (Q)

Ans:

Evaluate flux rectangular loop 1234 (Ans)

Evaluate Flux Rectangular Loop 1234 (Ans)

Evaluate flux rectangular loop 1234 (Ans)

For evaluating let us consider the rectangle 1234 to be made of strips of area each.

Using the relations obtained in Equations (1) and (2) and simplifying, we get

Rectangular loop 1234 xz plane

Rectangular Loop 1234 Xz Plane

Rectangular loop 1234 xz plane

(iv) For evaluating , let us consider the loop 1234 in yz plane as shown in Fig

.

Rectangular loop 1234 yz plane

Rectangular Loop 1234 Yz Plane

Rectangular loop 1234 yz plane

(3)

Now to evaluate , let us consider the rectangle 1234 to be made of strips of area hdz each.

(4)

In

Evaluate dl rectangular loop 1234 xz plane

Evaluate Dl Rectangular Loop 1234 Xz Plane

Evaluate dl rectangular loop 1234 xz plane

Using relations obtained in Equations (3) and (4) and simplifying, we get

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