The electric potential existing in spac is V(x,y,z,) = A (xy + yz +zx). (a) write the dimensional formula of A. (b) Find hte expression fr the electric field . (c) if A is 10 SI units, find the magnitude of the field at (1m, 1m, 1m)

Open in App

Solution

$V (x, y, z) A (x y + y z + z x) (a) A = [M T^{- 3} I^{- 1}] (b) d v = - E d r . i e . A (y + z) d x + A (z + x) d y + A (x + y) d z = - E (d x i + d y j + d z k) \Rightarrow [A (y + z) i + A (z + x) j + A (x + y) K] [d x \times i + d y j + d z k] = - E [d x i + d y j + s d z k]$
Equating now, we get,
$E = - A (y + z) i - A (z + x) j - A (x + y) k$
(c) $A = 10 S I u n i t, r = (1 m, 1 m, 1 m) E = - 10 (2) i - 10 (2) - 10 (2) k = - 20 i - 20 j - 20 k$
Magnitude
$| E | = \sqrt{(20^{2} + 20^{2} + 20^{2})} = \sqrt{1200} = 34.64 = 35 N / C$

Suggest Corrections

Similar questions

V (x, y, z) = A (x y + y z + z x)

10

(1 m, 1 m, 1 m)

V (x, y, z) = A (x y + y z + z x) .

V (x, y, z) = A (x y + y z + z x)

V (x, y, z) = A (x y + y z + z x)

A

V

P (x, y, z)

V = 4 x^{2} V

(1 m, 2 m)

Join BYJU'S Learning Program