four charges are placed at each corner of a square of side a . calculate force exerted at the centre of the square
Answers
Correct option is
B
4
−Q
(1+2
2
)
Let the side length of the square be a.
In △ACD,
⇒AD
2
+CD
2
=AC
2
⇒a
2
+a
2
=AC
2
⇒AC=
2
a
In △DOC,
⇒OD
2
+OC
2
=CD
2
⇒OC
2
+OC
2
=a
2
⇒OC=
2
a
Force on charge at C due to B,
F
1
=
a
2
KQ
2
where, K=
4πϵ
o
1
Force on charge at C due to D,
F
2
=
a
2
KQ
2
Force on charge at C due to A,
F
4
=
AC
2
KQ
2
=
2a
2
KQ
2
Force on charge at C due to q,
F
3
=
OC
2
KqQ
=
a
2
2KqQ
For the system to be equilibrium, net force acting at point C must be zero.
⇒
F
3
=
F
1
+
F
2
+
F
4
(Given:∣F
1
∣=∣F
2
∣)
⇒ ∣F
3
∣=
2
∣F
1
∣+∣F
4
∣
⇒
a
2
2KqQ
=
2
a
2
KQ
2
+
2a
2
KQ
2
⇒2q=
2
Q+
2
Q
⇒q=
4
Q
(1+2
2
). please mark me as brainlist and like me