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This post was last modified on 30 January 2020

MBBS 1st Year Physiology Most Important Questions From Last 10 Years (Common to all Universities)


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Maxwell's four equations are given as follows:

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?.D = ? ...(1)

?.B = 0 ...(2)

? × E = - ?B/?t ...(3)

? × H = J + ?D/?t ...(4)

However, D = e0E + P and B = µ0(H + M) where D = e0E + P

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J = sE

P = ?e0E

M = ?H

For Vacuum, we have ? = 0, J = 0

Maxwell's four equations simplify to the following form:

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?.E = 0 ...(5)

?.B = 0 ...(6)

? × E = - ?B/?t ...(7)

? × B = (1/c²) ?E/?t ...(8)

Maxwell's differential form in terms of electric and magnetic fields can be written as follows:

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E = E0 e^(i(?t - k.r)) ...(9)

B = B0 e^(i(?t - k.r)) ...(10)

Where,

r = xi + yj + zk = position vector

k = kx i + ky j + kz k

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These (E, B) must simultaneously obey equations (5) to (8).

From equation (5), we can write:

kxEx + kyEy + kzEz = 0 ...(11)

Similarly, from equation (6), we can write:

kxBx + kyBy + kzBz = 0 ...(12)

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Thus, electric field E ? k (direction of propagation)

Similarly, we can show that B can satisfy equation (6) only if

B ? k (electromagnetic wave)

To find relative orientation between E, B, k, we must validate equations (7) and (8) by the relations (9) and (10) of wave equation.

Now we can write:

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? × E = (?Ez/?y - ?Ey/?z)i + (?Ex/?z - ?Ez/?x)j + (?Ey/?x - ?Ex/?y)k

Now (? × E)x = ?Ez/?y - ?Ey/?z

From equation (9), we have:

?Ez/?y = i ky Ez

?Ey/?z = i kz Ey

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(? × E)x = i(kyEz - kzEy)

Similarly, we can find:

(? × E)y = i(kzEx - kxEz)

(? × E)z = i(kxEy - kyEx)

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Put values from equations (7) and (13), we get:

i(kxEy - kyEx) = - ?B/?t

Again from (10), we can show that:

?B/?t = i?B

Put values from equations (14) and (15) in (7), we get:

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i(k × E) = -i?B

or k × E = ?B

Equation (16) shows that B ? k and E.

From equations (5) and (6), it is clear that E, B, k are mutually perpendicular to each other.

Now, we can also satisfy equation (8) as follows:

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? × B = µ0J + µe0 ?E/?t

However, at low temperature of a polarizable dielectric medium:

J = -sE

We can see that:

? × B = i(k × B)

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?E/?t = i?E

Put these values in (8), we get:

i(k × B) = µ0(-sE) + µe0(i?E)

The equation above satisfies Maxwell's equation.

Hence electromagnetic

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