1.) What is the Magnitude of the electrostatic force on a +5 C charge 1.75 m to the left of a -2.5 C charge? (show your work)
2.) In What direction does the force on the +5 C charge act?
3.)Calculate the magnitude of the electric field of the -2.5 C charge at the location of the +5 c Charge.
4.) Calculate the magnitude of the total electric field at a point 2m above the +5 C charge. (superposition)
5.) Calculate the magnitude of the electrostatic potential at this point.
1,2). k =9•10⁹ N•m²/C²,
q₁=5 C, q₂= - 2.5 C.
F=k•q₁•|q₂|)/r² =
=9•10⁹•5•2.5/1.75² =3.67•10¹⁰ N (to the right).
3). E=k|q₂|/r² =9•10⁹•2.5/1.75²=
=7.35•10⁹ V/m(to the right).
4). E₁=k q₁/a² = 9•10⁹•5/2²=
=1.125•10¹⁰ V/m,
b=sqrt{2²+1.75²}=2.66 m,
E₂= k|q₂|/b² =
=9•10⁹•2.5/2.66²=3.18•10⁹ V/m.
cosα=2/2.66=0.75,
E=sqrt{E₁²+E₂²-2E₁E₂cosα} =
=sqrt{(1.125•10¹⁰)² +(3.18•10⁹)² -
-2•1.125•10¹⁰•3.18•10⁹•0.75} =
=9.13•10⁹ V/m.
5). φ=φ₁+φ₂ =k q₁/a + k q₂/b =
= k (q₁/a + q₂/b) =
= 9•10⁹(5/2 - 2.5/2.66) =1.4•10¹⁰ V.
1.) To calculate the magnitude of the electrostatic force between two charges, you can use Coulomb's Law. Coulomb's Law states that the electrostatic force (F) between two charges (q1 and q2) is given by the equation:
F = k * |q1 * q2| / r^2
where k is the electrostatic constant (k = 8.99 x 10^9 N * m^2 / C^2), q1 and q2 are the charges, and r is the distance between the charges.
For this problem, the charges are +5 C and -2.5 C, and the distance is 1.75 m. Plugging in the values, we get:
F = (8.99 x 10^9 N * m^2 / C^2) * |(+5 C) * (-2.5 C)| / (1.75 m)^2
Simplifying the calculation, we have:
F = (8.99 x 10^9 N * m^2 / C^2) * 12.5 C^2 / 3.0625 m^2
F = 36.287569 C * N
Therefore, the magnitude of the electrostatic force on the +5 C charge 1.75 m to the left of the -2.5 C charge is approximately 36.3 C * N.
2.) To determine the direction of the force on the +5 C charge, you can use the concept of electric field. The electric field is a vector quantity that describes the force experienced by a positive test charge at a particular location.
The direction of the force is given by the direction of the electric field at that point. In this case, since the -2.5 C charge is negative, the electric field points towards the charge. Hence, the force on the +5 C charge will act in the opposite direction, away from the -2.5 C charge.
3.) To calculate the magnitude of the electric field of the -2.5 C charge at the location of the +5 C charge, you can use the equation:
E = k * |q| / r^2
where E is the electric field, k is the electrostatic constant, q is the charge, and r is the distance between the charges.
In this case, the charge is -2.5 C and the distance is 1.75 m. Plugging in the values, we have:
E = (8.99 x 10^9 N * m^2 / C^2) * (|-2.5 C|) / (1.75 m)^2
Simplifying the calculation, we get:
E = (8.99 x 10^9 N * m^2 / C^2) * 2.5 C / 3.0625 m^2
E = 36.287569 N / C
Therefore, the magnitude of the electric field of the -2.5 C charge at the location of the +5 C charge is approximately 36.3 N / C.
4.) To calculate the magnitude of the total electric field at a point 2m above the +5 C charge, we need to consider the superposition principle. The superposition principle states that the total electric field at a point due to multiple charges is the vector sum of the electric fields produced by each individual charge.
In this case, we have only one charge (+5 C) and want to find the electric field at a point 2m above it. The electric field due to a point charge can be calculated using the equation:
E = k * |q| / r^2
where E is the electric field, k is the electrostatic constant, q is the charge, and r is the distance from the charge.
Plugging in the values, we have:
E = (8.99 x 10^9 N * m^2 / C^2) * (|+5 C|) / (2 m)^2
Simplifying the calculation, we get:
E = (8.99 x 10^9 N * m^2 / C^2) * 5 C / 4 m^2
E = 11.23753125 N / C
Therefore, the magnitude of the electric field at a point 2m above the +5 C charge is approximately 11.2 N / C.
5.) To calculate the magnitude of the electrostatic potential at a point, you can use the equation:
V = k * |Q| / r
where V is the electrostatic potential, k is the electrostatic constant, Q is the charge, and r is the distance from the charge.
Using the given values, we have:
V = (8.99 x 10^9 N * m^2 / C^2) * (|+5 C|) / 2 m
Simplifying the calculation, we get:
V = (8.99 x 10^9 N * m^2 / C^2) * 5 C / 2 m
V = 22.475 x 10^9 N * m / C
Therefore, the magnitude of the electrostatic potential at the given point is approximately 22.5 x 10^9 N * m / C.