Q. 604.3( 3 Votes )

The electric potential existing in space is
V(x, y, z) = A (xy + yz + zx).

(a) Write the dimensional formula of A.

(b) Find the expression for the electric field.

(c) If A is 10 SI units, find the magnitude of the electric filed at (1m, 1m, 1m).


Answer :


Given:
Electric Potential :V(x,y,z) = A (xy + yz + zx).
A = 10 SI units.
Formula used:
(a)
From the given data V(x,y,z) = A (xy + yz + zx), we can say that Voltage is the product of A and length2(xy+yz+zx)
Volt = A× m2We know that Volt = , where Q=

Thus, dimensions of A are
(b)
Formula for electric field is:
Where


Hence , expression of electric field is
(c)
A = 10 SI units
(x,y,z) = (1m,1m,1m)
Substituting in the expression of E we get:

Magnitude of Electric field is



Hence, magnitude of Electric field at (1m,1m,1m0 is 34.64 NC-1.


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