The electric potential in a given space is represented by V= 3x + 5y - 6z. Show that the electric field intensity is uniform everywhere in the given space.
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Answer:Given, V=k[2x
2
−y
2
+z
2
]
Electric field ,
E
=−(
dx
dV
i
^
+
dy
dV
j
^
+
dz
dV
k
^
)
or,
E
=−k(4x
i
^
−2y
j
^
+2z
k
^
)
or,
E
(1,1,1)
=−k(4
i
^
−2
j
^
+2
k
^
)
Magnitude of electric field=∣
E
(1,1,1)
∣=
k
2
(16+4+4)
=k
24
=2k
6
Explanation:
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