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KVPY SA Exam 19-Nov-2017 Question Paper
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© examsnet.com
Question : 22
Total: 80
A total charge q is divided as
q
1
and
q
2
which are kept at two of the vertices of an equilateral triangle of side a. The magnitude of the electric field E at the third vertex of the triangle is to be depicted schematically as a function of
x
=
q
1
q
. Choose the correct figure.
Validate
Solution:
E
net
=
→
E
1
+
→
E
2
q
=
q
1
+
q
2
|
→
E
net
|
=
√
(
k
q
1
a
)
2
+
(
k
q
2
a
)
2
+
2
k
2
q
1
q
2
a
2
.
cos
60
°
E
net
=
k
a
√
q
1
2
+
q
2
2
+
q
1
q
2
E
net
=
k
a
√
q
1
2
+
(
q
−
q
1
)
2
+
q
1
(
q
−
q
1
)
=
k
a
q
×
√
(
q
1
q
)
2
+
1
2
+
(
q
1
q
)
2
−
2
q
1
q
+
q
1
q
−
q
1
2
q
2
=
k
a
q
√
x
2
+
1
−
x
E
net
=
k
a
q
(
√
(
x
−
1
2
)
2
+
3
4
)
Minima must be at
|
x
=
1
2
|
© examsnet.com
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