What is the acceleration vector of the negative charge from the example above if its charge is 250 me and its mass is 750 9? The gravitational force and force due to air resistance are negligible compared to the electrostatic force so they can be ignored.
To find the acceleration vector of the negative charge, we need to use the equation of motion for an object under the influence of an electrostatic force.
The electrostatic force is given by Coulomb's law:
Fe = k * (q1 * q2) / r^2
where Fe is the electrostatic force, k is the Coulomb's constant, q1 and q2 are the charges, and r is the distance between the charges.
In our example, the negative charge has a charge of 250 me (millielectrons) and is under the influence of an electrostatic force.
Since the gravitational force and force due to air resistance are negligible compared to the electrostatic force, we can ignore them.
Therefore, the equation of motion is:
Fe = m * a
where m is the mass of the negative charge and a is the acceleration.
Substituting Fe with the electrostatic force:
k * (q1 * q2) / r^2 = m * a
Rearranging the equation to solve for acceleration a:
a = (k * q1 * q2) / (m * r^2)
Plugging in the values:
k = 9 x 10^9 Nm^2/C^2 (Coulomb's constant)
q1 = charge of the negative charge = 250 me = 250 * 1.6 x 10^(-19) C (millielectrons converted to Coulombs)
q2 = charge of the positive charge = 250 me = 250 * 1.6 x 10^(-19) C (millielectrons converted to Coulombs)
m = mass of the negative charge = 750 g = 750 * (1/1000) kg (grams converted to kilograms)
r = distance between the charges (not given)
Let's assume that the distance between the charges is 1 meter (r = 1 m) for simplicity.
Now, we can calculate the acceleration vector a:
a = (9 x 10^9 Nm^2/C^2 * (250 * 1.6 x 10^(-19) C) * (250 * 1.6 x 10^(-19) C)) / (750 * (1/1000) kg * (1 m)^2)
Simplifying the equation gives the acceleration vector of the negative charge.
To find the acceleration vector of the negative charge, we first need to determine the electrostatic force acting on it. The electrostatic force between two charges can be calculated using Coulomb's law:
F = (k * |q1 * q2|) / r^2
Where:
F is the electrostatic force between the charges
k is the electrostatic constant (9x10^9 N m^2/C^2)
q1 and q2 are the charges
r is the distance between the charges
In this case, the electrostatic force acting on the negative charge would be the force exerted by the positive charge. Since the positive charge is 600 μC (600 x 10^-6 C) and the negative charge is 250 μC (250 x 10^-6 C), we can rewrite Coulomb's law as:
F = (k * |250 μC * 600 μC|) / r^2
Next, we need to calculate the mass of the negative charge. It is given as 750 x 10^-9 kg.
Once we know the electrostatic force and the mass of the negative charge, we can use Newton's second law of motion to find the acceleration:
F = m * a
Where:
F is the force
m is the mass
a is the acceleration
Now, let's plug in the values and calculate the acceleration vector.
To find the acceleration vector of the negative charge, we need to use the formula of electrostatic force:
\[F_{elec} = q \cdot E\]
where:
- \(F_{elec}\) is the electrostatic force acting on the charge,
- \(q\) is the charge of the negative charge, and
- \(E\) is the electric field vector.
The acceleration of the charge \(a\) is given by Newton's second law:
\[F_{elec} = m \cdot a\]
where:
- \(m\) is the mass of the charge.
Since the gravitational and air resistance forces are negligible, we can focus solely on the electrostatic force. Now let's calculate the electric field vector \(E\):
The electric field vector \(E\) at a point in space is defined as the force per unit charge that would be experienced by a positive test charge placed at that point.
So, to calculate the electric field vector \(E\), we need to know the properties of the source charge. Unfortunately, the properties of the source charge are not provided in the question. Therefore, we do not have enough information to determine the electric field vector and subsequently the acceleration vector of the negative charge.