2) Two point charges, Q1 = 5.00 nC and Q2 = -3.00 nC, are separated by 35.0 cm. (a) What is the potential energy of the pair? What is the significance of the algebraic sign of your answer? (b) What is the electric potential at a point midway between the charges?
can you please help me with the answer
To find the potential energy of the pair of charges, we can use the formula for potential energy in an electric field:
PE = k * (Q1 * Q2) / r
where PE is the potential energy, k is the Coulomb's constant (9.0 x 10^9 Nm^2/C^2), Q1 and Q2 are the charges, and r is the separation between the charges.
(a) To find the potential energy of the pair, we can substitute the given values into the formula:
PE = (9.0 x 10^9 Nm^2/C^2) * (5.00 x 10^-9 C) * (-3.00 x 10^-9 C) / 0.35 m
Simplifying this calculation, we get:
PE = -0.771 J
The significance of the algebraic sign of the answer is that it indicates the potential energy of the charges is negative. This means that work would need to be done externally to bring the charges together from infinity, or equivalently, there is an attractive force between the two charges.
(b) To find the electric potential at a point midway between the charges, we can use the formula for electric potential due to a point charge:
V = k * (Q / r)
where V is the electric potential, k is the Coulomb's constant, Q is the charge, and r is the distance from the charge.
In this case, the charges are equal in magnitude but opposite in sign, so they cancel each other out at the midpoint. Thus, the electric potential at the point midway between the charges is zero.
To begin, we can use the formula for electric potential energy to calculate the potential energy of the pair.
(a) The formula for the electric potential energy (PE) of two point charges is given by:
PE = (k * |Q1 * Q2|) / r
where k is the electrostatic constant (k = 8.99 x 10^9 N m^2/C^2), Q1 and Q2 are the magnitudes of the charges, and r is the separation distance between the charges.
Substituting the given values into the formula:
Q1 = 5.00 nC = 5.00 x 10^(-9) C (converting from nanoCoulombs to Coulombs)
Q2 = -3.00 nC = -3.00 x 10^(-9) C
r = 35.0 cm = 0.35 m (converting from centimeters to meters)
PE = (8.99 x 10^9 N m^2/C^2) * |(5.00 x 10^(-9) C) * (-3.00 x 10^(-9) C)| / 0.35 m
Simplifying further,
PE = (8.99 x 10^9 N m^2/C^2) * (1.50 x 10^(-17) C^2) / 0.35 m
Using a calculator, we find:
PE ≈ -386.57 J
The algebraic sign of the potential energy (-386.57 J) indicates the nature of the interaction between the charges. A negative value signifies that the charges are of opposite sign and that work would be done to bring the charges closer to each other.
(b) To find the electric potential at a point midway between the charges, we can use the formula for electric potential.
The formula for electric potential (V) at a point due to a point charge is given by:
V = (k * |Q|) / r
where Q is the charge and r is the distance from the charge.
Considering only Q1 = 5.00 nC for this calculation, and the distance is half the separation distance between the charges (0.5 * 35.0 cm).
Q1 = 5.00 nC = 5.00 x 10^(-9) C
r = 0.5 * 0.35 m = 0.175 m
V = (8.99 x 10^9 N m^2/C^2) * (5.00 x 10^(-9) C) / 0.175 m
Simplifying further,
V ≈ 2.57 x 10^7 V
Therefore, the electric potential at a point midway between the charges is approximately 2.57 x 10^7 volts.