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Physics
Physics
Problem
The electric potential at a point
(
x
,
y
,
z
)
(x, y, z)
(
x
,
y
,
z
)
is given by
V
=
−
x
2
y
−
x
z
3
+
4
V = -x^2y - xz^3 + 4
V
=
−
x
2
y
−
x
z
3
+
4
. The electric field
E
⃗
\vec{E}
E
at that point is: (2009) a.
E
⃗
=
i
^
2
x
y
+
j
^
(
x
2
+
y
2
)
+
k
^
(
2
x
y
−
y
2
)
\vec{E} = \hat{i}2xy + \hat{j}(x^2 + y^2) + \hat{k}(2xy - y^2)
E
=
i
^
2
x
y
+
j
^
(
x
2
+
y
2
)
+
k
^
(
2
x
y
−
y
2
)
b.
E
⃗
=
i
^
z
3
+
j
^
x
y
z
+
k
^
z
2
\vec{E} = \hat{i}z^3 + \hat{j}xyz + \hat{k}z^2
E
=
i
^
z
3
+
j
^
x
y
z
+
k
^
z
2
c.
E
⃗
=
i
^
(
2
x
y
+
z
3
)
+
j
^
x
y
2
+
k
^
3
z
2
x
\vec{E} = \hat{i}(2xy + z^3) + \hat{j}xy^2 + \hat{k}3z^2x
E
=
i
^
(
2
x
y
+
z
3
)
+
j
^
x
y
2
+
k
^
3
z
2
x
d.
E
⃗
=
i
^
(
2
x
y
+
z
3
)
+
j
^
x
2
+
k
^
3
x
z
2
\vec{E} = \hat{i}(2xy + z^3) + \hat{j}x^2 + \hat{k}3xz^2
E
=
i
^
(
2
x
y
+
z
3
)
+
j
^
x
2
+
k
^
3
x
z
2
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