Let E : E,i + Ej+ E,k and H:= H,i + Hyj+ H,k be two vectors assumed to have continuous partial derivatives (of second order at least) with respect to position and time. Suppose further that E and H satisfy the equations: 1 JE c dt 1 Эн V.E = 0, V-H = 0, V×E = V×H= с де prove that E and H satisfy the equation 1 a? E; c2 Ət2 1 a? H; c2 Ət2 v²E; = and VH = Here, i = x, y or z. Hint: Use the fact that V x (V x V) =V (V · V) – V²v.
Let E : E,i + Ej+ E,k and H:= H,i + Hyj+ H,k be two vectors assumed to have continuous partial derivatives (of second order at least) with respect to position and time. Suppose further that E and H satisfy the equations: 1 JE c dt 1 Эн V.E = 0, V-H = 0, V×E = V×H= с де prove that E and H satisfy the equation 1 a? E; c2 Ət2 1 a? H; c2 Ət2 v²E; = and VH = Here, i = x, y or z. Hint: Use the fact that V x (V x V) =V (V · V) – V²v.
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Transcribed Image Text:Let E := E,i + E,j+ E,k and H :=
least) with
= H„i + Hyj+H̟k be two vectors assumed to have continuous partial derivatives (of second order at
respect to position and time. Suppose further that E and H satisfy the equations:
1 Эн
1 ОЕ
V·E = 0, V·H = 0, V×E =
V×H=
c dt
c dt
prove that E and H satisfy the equation
v'E;
1 a?E;
and V² H; =
1 0? Н,
c2 Ət2
c2 at2
Here, i = x, y or z.
Hint: Use the fact that
V × (V × V) = V (V . V) – V²v.
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