a. A 25 nC particle and a – 7 nC particle is interacting with each other at a certain distance. Find the force between the two charges @ 3.0 cm and 1.0 cm
Calculate and draw each of the particle’s electric fields.
Calculate the electric potential values of the two particles.
Calculate the electric potential energies of the two particles.
To find the force between two charged particles, we can use Coulomb's Law:
F = k * (q1 * q2) / r^2
where F is the force between the particles, k is Coulomb's constant (9 x 10^9 N m^2/C^2), q1 and q2 are the charges of the particles, and r is the distance between them.
a)
For the 25 nC and -7 nC particles at a distance of 3.0 cm:
q1 = 25 nC = 25 x 10^-9 C
q2 = -7 nC = -7 x 10^-9 C
r = 3.0 cm = 3.0 x 10^-2 m
Plugging in the values into Coulomb's Law, we have:
F = (9 x 10^9 N m^2/C^2) * (25 x 10^-9 C) * (-7 x 10^-9 C) / (3.0 x 10^-2 m)^2
Calculating this will give you the force between the two charges.
b)
To calculate the electric field, we can use the formula:
E = F / q
where E is the electric field, F is the force, and q is the charge that experiences the electric field.
For the 25 nC particle, we can calculate the electric field at a given distance by using the force calculated in part a) divided by the charge of the 25 nC particle (q1).
E1 = F / q1
Similarly, for the -7 nC particle, we can calculate the electric field at a given distance by using the force calculated in part a) divided by the charge of the -7 nC particle (q2).
E2 = F / q2
Calculate these two values to find the electric fields.
c)
The electric potential is given by the formula:
V = k * q / r
where V is the electric potential, k is Coulomb's constant, q is the charge, and r is the distance from the charge.
For the 25 nC particle, we can calculate the electric potential at a distance of 1.0 cm by using the charge q1.
V1 = (9 x 10^9 N m^2/C^2) * (25 x 10^-9 C) / (1.0 x 10^-2 m)
Similarly, for the -7 nC particle, we can calculate the electric potential at a distance of 1.0 cm by using the charge q2.
V2 = (9 x 10^9 N m^2/C^2) * (-7 x 10^-9 C) / (1.0 x 10^-2 m)
Calculate these two values to find the electric potential.
d)
Finally, to calculate the electric potential energy, we can use the formula:
PE = q * V
where PE is the electric potential energy, q is the charge, and V is the electric potential.
For the 25 nC particle, the electric potential energy can be calculated by multiplying the charge q1 by the electric potential V1.
PE1 = (25 x 10^-9 C) * V1
Similarly, for the -7 nC particle, the electric potential energy can be calculated by multiplying the charge q2 by the electric potential V2.
PE2 = (-7 x 10^-9 C) * V2
Calculate these two values to find the electric potential energies of the particles.