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Q1) [13p] Three charges are placed at the corners of an equilateral triangle of side 2.0 cm as shown. a) Mark the electric forces due to charges $Q_2$ and $Q_3$ on charge $Q_1$ and find the net force on $Q_1$.[3] b) What is the net electric field at the position of $Q_1$ due to charges $Q_2$ and $Q_3$? [1] c) Another charge 'q' is brought from infinity with constant speed and placed at point P (half way between $Q_2$ and $Q_3$). As a result, the net force on $Q_1$ (1.0 nC) is zero. What is the sign and magnitude of charge q? (Show all forces acting on $Q_1$ and show all the steps clearly.) [3] d) What is the net electric potential at point P with respect to infinity? [3] e) What is the work done by an external force in this process of bringing q to point P from infinity? [1] f) What is the electric potential energy of the system $Q_1$, $Q_2$, and $Q_3$? [2]

          Q1) [13p] Three charges are placed at the corners of an equilateral triangle of side 2.0 cm as shown.
a) Mark the electric forces due to charges $Q_2$ and $Q_3$ on charge $Q_1$ and find the net force on $Q_1$.[3]
b) What is the net electric field at the position of $Q_1$ due to charges $Q_2$ and $Q_3$? [1]
c) Another charge 'q' is brought from infinity with constant speed and placed at point P (half way between $Q_2$ and $Q_3$). As a result, the net force on $Q_1$ (1.0 nC) is zero. What is the sign and magnitude of charge q? (Show all forces acting on $Q_1$ and show all the steps clearly.) [3]
d) What is the net electric potential at point P with respect to infinity? [3]
e) What is the work done by an external force in this process of bringing q to point P from infinity? [1]
f) What is the electric potential energy of the system $Q_1$, $Q_2$, and $Q_3$? [2]

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Q1) [13p] Three charges are placed at the corners of an equilateral triangle of side 2.0 cm as shown.
a) Mark the electric forces due to charges Q2 and Q3 on charge Q1 and find the net force on Q1.[3]
b) What is the net electric field at the position of Q1 due to charges Q2 and Q3? [1]
c) Another charge 'q' is brought from infinity with constant speed and placed at point P (half way between Q2 and Q3). As a result, the net force on Q1 (1.0 nC) is zero. What is the sign and magnitude of charge q? (Show all forces acting on Q1 and show all the steps clearly.) [3]
d) What is the net electric potential at point P with respect to infinity? [3]
e) What is the work done by an external force in this process of bringing q to point P from infinity? [1]
f) What is the electric potential energy of the system Q1, Q2, and Q3? [2]

Added by Rodrigo S.

University Physics with Modern Physics

Hugh D. Young 14th Edition

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Solved by Expert Sri K

10/06/2023

Step 1

Coulomb's law states that the electric force between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. The electric force between charges Q and Q is given by: F(Q, Q) = k * Show more…

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Q1) [13p] Three charges are placed at the corners of an equilateral triangle of side 2.0 cm as shown. a) Mark the electric forces due to charges Q2 and Q3 on charge Q1 and find the net force on Q1.[3] b) What is the net electric field at the position of Q1 due to charges Q2 and Q3? [1] c) Another charge 'q' is brought from infinity with constant speed and placed at point P (half way between Q2 and Q3). As a result, the net force on Q1 (1.0 nC) is zero. What is the sign and magnitude of charge q? (Show all forces acting on Q1 and show all the steps clearly.) [3] d) What is the net electric potential at point P with respect to infinity? [3] e) What is the work done by an external force in this process of bringing q to point P from infinity? [1] f) What is the electric potential energy of the system Q1, Q2, and Q3? [2]

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Transcript

00:01 For this question, solution here is, here from the above figure that here this is the charge 1, this is the charge 2 and this is the charge 3.

00:13 Here 3 charges is given making the angle 60 degree.

00:17 Here from the charge 1, here the force f2 to the charge q2 and this is the energy e3 to the charge 3 and the force f3.

00:32 Here on first charge, the charge is 1 nano coulomb.

00:36 On charge 2nd here, this is minus 2 nano coulomb and on the charge 3rd, there is minus 2 nano coulomb also.

00:45 Now for the e part, here the electrical force on q1 due to q2, here electric force on charge q1 due to charge q2, here f2 is equal to k multiply to q1 multiply to q2 divided by r.

01:11 Now substituting the value, here f1 is equal to 4 .5 multiply to 10 to the power minus 5 newton in the direction shown above.

01:25 Now the force on charge q1 due to charge q3, here this is force 3 is equal to k multiply to q1 multiply to q3 divided by a square.

01:41 Now from this, here we know that 4 .5 multiply to 10 to the power minus 5 newton.

01:49 Now in the direction shown in the diagram.

01:52 Now here we know that the total force, the net force, here it is f2 plus f3 multiply to sin 60.

02:05 Now from this, here we get that 7 .8 multiply to 10 to the power minus 5 newton.

02:15 Now by further solving for the b part, here the electric force at q1 due to q2, here it is e2 is equal to k multiply to q2 divided by a square which is equal to here 4 .5 multiply to 10 to the power 4 volt per meter in the direction shown in the figure.

02:41 Here q3 is also equal in magnitude but its own direction is shown...

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