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Question : 11
Total: 26
SECTION -C
Four point charges
Find the
(a) resultant electric force on a charge
(b) potential energy of this system.
OR
(a) Three point charges
(b) Find out the amount of the work done to separate the charges at infinite distance.
Solution:
(a) Finding the resultant force on a charge Q
(b) Potential Energy of the system
(a) Let us find the force on the chargeQ
F 1 =
=
(
) (along A C )
Force due to the chargeq B
F 2 =
along B C
Force due to the chargeq D
F 3 =
along D C
Resultant of these two equal forces
Force due to the other chargeQ
F 23 =
(along A C )
∴ Q C
F = F 1 + F 23 =
[
+ √ 2 q ]
This force is directed alongA C
(For the chargeQ A C A
[Note : Don't deduct marks if the student does not write the direction of the net force,F ]
(b) Potential energy of the system
=
[ 4
+
+
]
=
[ 4 q Q +
+
]
OR
(a) Finding the magnitude of the resultant force on chargeq
(b) Finding the work done
(a) Force on chargeq − 4 q
F 1 =
(
) , along A B
Force on the chargeq 2 q
F 2 =
(
) , along C A
The forcesF 1 F 2 120 ∘
Hence, resultant electric force on chargeq
F = √ F 1 2 + F 2 2 + 2 F 1 F 2 cos θ
= √ F 1 2 + F 2 2 + 2 F 1 F 2 cos 120 ∘
= √ F 1 2 + F 2 2 − F 1 F 2
= (
) √ 16 + 4 − 8
=
(
)
(b) Net P.E. of the system
=
⋅
[ − 4 + 2 − 8 ]
=
∴ Work done =
=
(b) Potential Energy of the system
(a) Let us find the force on the charge
Force due to the charge
Force due to the charge
Resultant of these two equal forces
Force due to the other charge
This force is directed along
(For the charge
[Note : Don't deduct marks if the student does not write the direction of the net force,
(b) Potential energy of the system
OR
(a) Finding the magnitude of the resultant force on charge
(b) Finding the work done
(a) Force on charge
Force on the charge
The forces
Hence, resultant electric force on charge
(b) Net P.E. of the system
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