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iTeachChem
•
2y ago
Keshav
Gauss's Law(differential form)
How can we use differential form of Gauss
's law for this qs
?
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I
iTeachChem Helper
•
6/2/24, 6:55 AM
@Gyro Gearloose
I
iTeachChem Helper
•
6/2/24, 6:55 AM
Note for OP
+solved @user
+solved @user
to close the thread when your doubt is solved
. Mention the user who helped you solve the doubt
. This will be added to their stats
.
K
Keshav
OP
•
6/2/24, 6:56 AM
$
$
\nabla
\cdot
\vec
{E
}
=
\frac
{
\rho
}
{
\epsilon
_
{0
}
}
$
$
O
Opt
•
6/2/24, 6:56 AM
Oh that
's an amazing one
T
TeXit
•
6/2/24, 6:56 AM
Keshav
K
Keshav
OP
•
6/2/24, 6:56 AM
how to use this
O
Opt
•
6/2/24, 6:58 AM
Just a sec writing it down
K
Keshav
How can we use differential form of Gauss's law for this qs?
K
Keshav
OP
•
6/2/24, 6:58 AM
btw they have missed something
$
$
\vec
{E
}
=
\frac
{a
(x
\hat
{i
}
+y
\hat
{j
}
)
}
{x
^2
+y
^2
}
$
$
T
TeXit
•
6/2/24, 6:58 AM
Keshav
K
Keshav
OP
•
6/2/24, 6:59 AM
this is the given expression
O
Opt
Just a sec writing it down
K
Keshav
OP
•
6/2/24, 7:02 AM
ohk
O
Opt
•
6/2/24, 7:02 AM
Oh there
's an a
K
Keshav
OP
•
6/2/24, 7:03 AM
that won
't change a lot of things
O
Opt
•
6/2/24, 7:03 AM
Wait
, is it necessary to use differential form
? I
'm using integral form rn
. Just a sec
K
Keshav
OP
•
6/2/24, 7:03 AM
uh
, ik how to solve this using integral form
but was curious if we can use differential form as we have the expression for Electric field
K
Keshav
OP
•
6/2/24, 7:06 AM
@Opt
O
Opt
•
6/2/24, 7:10 AM
Hmm I
'm having trouble with the final integral
O
Opt
•
6/2/24, 7:10 AM
What did you get divergence of
E
to be
?
K
Keshav
OP
•
6/2/24, 7:14 AM
$
$div
\cdot
\vec
{E
}
=
\frac
{
\partial E
{x
}
}
{
\partial x
}
+
\frac
{
\partial E
{y
}
}
{
\partial y
}
$
$
T
TeXit
•
6/2/24, 7:14 AM
Keshav
K
Keshav
OP
•
6/2/24, 7:16 AM
bhai
@Opt div 0 aa rha
check kr toh
T
TeXit
**Keshav**
O
Opt
•
6/2/24, 7:16 AM
Not this
. I mean the final value
.
K
Keshav
bhai @Opt div 0 aa rha 💀 check kr toh
O
Opt
•
6/2/24, 7:17 AM
Haan because origin pe infinite charge banega
K
Keshav
OP
•
6/2/24, 7:17 AM
so this doesn
't works
K
Keshav
OP
•
6/2/24, 7:19 AM
@Opt so is it impossible to use this equation
?
O
Opt
•
6/2/24, 7:20 AM
Mostly
O
Opt
•
6/2/24, 7:20 AM
Divergence is infinite at origin
.
$
$
\frac
{4
}
{x
^2
+y
^2
}
$
$
T
TeXit
•
6/2/24, 7:21 AM
Opt
K
Keshav
OP
•
6/2/24, 7:21 AM
4
/x
^2
+y
^2
?
?
O
Opt
•
6/2/24, 7:22 AM
Yup
O
Opt
•
6/2/24, 7:22 AM
Wahi toh aata hai differentiation karne par
, right
?
K
Keshav
OP
•
6/2/24, 7:23 AM
mera result 0 aa rha tha
O
Opt
•
6/2/24, 7:23 AM
$
$
\nabla
$
$
O
Opt
•
6/2/24, 7:23 AM
Ok I haven
't used LaTex before
. Need to learn
.
T
TeXit
•
6/2/24, 7:23 AM
Opt
O
Opt
•
6/2/24, 7:24 AM
Anyways
, zero nahi aata
O
Opt
•
6/2/24, 7:24 AM
Varying with distance from origin
. No chance the divergence is zero
.
O
Opt
•
6/2/24, 7:25 AM
Distance from z
-axis sorry
K
Keshav
OP
•
6/2/24, 7:25 AM
ok so if you result is correct what next
?
$
$
\rho
=
\frac
{Q
}
{4
\pi a
^2
}
$
$
T
TeXit
•
6/2/24, 7:25 AM
Keshav
O
Opt
•
6/2/24, 7:25 AM
Nope
. That
's wrong
K
Keshav
OP
•
6/2/24, 7:25 AM
oh yeah
O
Opt
•
6/2/24, 7:26 AM
You have to integrate on the volume
. Directly substituting is impossible
.
K
Keshav
OP
•
6/2/24, 7:27 AM
its making it harder lol
ig this equation is just making things harder for us
O
Opt
•
6/2/24, 7:27 AM
Yeah integral form is probably best here
O
Opt
•
6/2/24, 7:27 AM
Because origin is out of the equation if you only consider surface integral
K
Keshav
OP
•
6/2/24, 7:28 AM
yup
O
Opt
•
6/2/24, 7:28 AM
No zeroes in denominator
.
K
Keshav
OP
•
6/2/24, 7:28 AM
+solved
@Opt
I
iTeachChem Helper
•
6/2/24, 7:28 AM
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(1082354613749035099
)
Time
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(763645886500175892
)
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