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A +Q and a +2Q point charges were placed at the vertices of an

equilateral triangle of side a, A third —2Q charge is placed at point P.
What is the work done by an external force in moving —2Q from a position at

infinity to P?
The work done by an external force in moving a point charge from infinity to a point in the field of other charges is equal to the change in its potential energy. The potential energy of a point charge Q at a point in an electric field is given by:

U = QV

where V is the electric potential at that point. The electric potential at a point in the field of other charges is the work done per unit charge by an external force in bringing a small positive test charge from infinity to that point. It is defined as:

V = W/Q

where W is the work done by an external force in bringing the test charge from infinity to that point.

In this problem, we can find the electric potential at point P due to the charges +Q and +2Q by summing the contributions from each charge. The electric potential at a point in the field of a point charge Q is given by:

V_Q = kQ/r

where k is the Coulomb constant and r is the distance between the point charge and the point at which the potential is being calculated.

At point P, the distance between +Q and -2Q is a, and the distance between +2Q and -2Q is 2a. Using the principle of superposition, the electric potential at point P due to the charges +Q and +2Q is:

V_P = kQ/a + k(2Q)/(2a)

= kQ/a + kQ/a

= 2kQ/a

The electric potential at infinity is zero, since there are no charges present at infinity. Therefore, the change in potential energy of the charge -2Q as it is moved from infinity to point P is:

ΔU = QΔV

= -2Q(2kQ/a)

= -4kQ^2/a

Since the charge -2Q is negative, the work done by an external force in moving it from infinity to point P is positive. Therefore, the work done by an external force in moving the charge -2Q from infinity to point P is:

W = -ΔU

= 4kQ^2/a

= (1/4πε₀)(Q^2/a)

where ε₀ is the permittivity of free space.

Therefore, the work done by an external force in moving the charge -2Q from infinity to point P is (1/4πε₀)(Q^2/a).
 
The work done by an external force in moving a point charge from infinity to a point in the field of other charges is equal to the change in its potential energy. The potential energy of a point charge Q at a point in an electric field is given by:

U = QV

where V is the electric potential at that point. The electric potential at a point in the field of other charges is the work done per unit charge by an external force in bringing a small positive test charge from infinity to that point. It is defined as:

V = W/Q

where W is the work done by an external force in bringing the test charge from infinity to that point.

In this problem, we can find the electric potential at point P due to the charges +Q and +2Q by summing the contributions from each charge. The electric potential at a point in the field of a point charge Q is given by:

V_Q = kQ/r

where k is the Coulomb constant and r is the distance between the point charge and the point at which the potential is being calculated.

At point P, the distance between +Q and -2Q is a, and the distance between +2Q and -2Q is 2a. Using the principle of superposition, the electric potential at point P due to the charges +Q and +2Q is:

V_P = kQ/a + k(2Q)/(2a)

= kQ/a + kQ/a

= 2kQ/a

The electric potential at infinity is zero, since there are no charges present at infinity. Therefore, the change in potential energy of the charge -2Q as it is moved from infinity to point P is:

ΔU = QΔV

= -2Q(2kQ/a)

= -4kQ^2/a

Since the charge -2Q is negative, the work done by an external force in moving it from infinity to point P is positive. Therefore, the work done by an external force in moving the charge -2Q from infinity to point P is:

W = -ΔU

= 4kQ^2/a

= (1/4πε₀)(Q^2/a)

where ε₀ is the permittivity of free space.

Therefore, the work done by an external force in moving the charge -2Q from infinity to point P is (1/4πε₀)(Q^2/a).


The current I (in amperes) through a section of wire varies with

time t (in seconds) given by the function 1 (t) = At^2 — Bt, where A

0.90 A/s^2 and B = O.040 A/s^2.

How much charge has flown in the given section from t = 1.0 s to t = 3.0 s?
 
The theory that follows the concept that the greatest amount of good should serve the greatest amount of people is known as

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The theory that follows the concept that the greatest amount of good should serve the greatest amount of people is known as utilitarianism. Utilitarianism is a moral theory that holds that the best action is the one that maximizes overall happiness or pleasure and minimizes overall pain or suffering for the greatest number of people. This ethical approach was developed by philosophers such as Jeremy Bentham and John Stuart Mill in the 19th century and remains widely discussed and debated in the fields of ethics, political science, and philosophy.
 
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