Question

What represent(s) the electrostatic field
a- E=yi+xj
b-E=yi
c-E=yi+xj+zk
d-E=alpha*r (alpha=constant)

Answer 1

Explanation:

We will consider vectors in 3D, though the notation we shall introduce applies (mostly)

just as well to n dimensions. For a general vector

x = (x1, x2, x3)

we shall refer to xi

, the i

th component of x. The index i may take any of the values

1, 2 or 3, and we refer to “the vector xi” to mean “the vector whose components are

(x1, x2, x3)”. However, we cannot write x = xi

, since the LHS is a vector and the RHS a

scalar. Instead, we can write [x]i = xi

, and similarly [x + y]i = xi + yi

.

Note that the expression yi = xi

implies that y = x; the statement in suffix notation

is implicitly true for all three possible values of i (one at a time!).

Einstein introduced a convention whereby if a particular suffix (e.g., i) appears twice

in a single term of an expression then it is implicitly summed. For example, in traditional

notation

x . y = x1y1 + x2y2 + x3y3 =

X

3

i=1

xiyi

;

using summation convention we simply write

x . y = xiyi

.

All we are doing is not bothering to write down the P!

The Rules of Summation Convention

Summation convention does not allow any one suffix to appear more than twice within

a single term; so xiyizi

is meaningless. We have to take care to avoid this: for example,

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