the following point charges are placed on the x-axis: +2.0μC at x=20cm,-3.0μC at x=30cm and -4.0μC at x=40cm. What is the potential at x=0?
To find the electric potential at x=0, we can use the principle of superposition. The electric potential at any point due to a system of charges is the algebraic sum of the potentials due to each individual charge.
The formula to calculate the electric potential due to a point charge is given by V = k * q / r, where V is the electric potential, k is the Coulomb's constant (9 x 10^9 Nm^2/C^2), q is the charge, and r is the distance between the point charge and the location where the potential is being calculated.
Given the charges and their positions on the x-axis:
1. Charge 1: +2.0μC at x=20cm (or 0.20m)
2. Charge 2: -3.0μC at x=30cm (or 0.30m)
3. Charge 3: -4.0μC at x=40cm (or 0.40m)
To find the electric potential at x=0, we need to calculate the potential due to each charge individually and then find their sum:
Potential due to Charge 1:
V1 = (9 x 10^9 Nm^2/C^2) * (2.0 x 10^-6 C) / (0.20m - 0m) [Using the formula V = k * q / r]
V1 = 9 x 10^9 Nm^2/C^2 * 10 C / 0.20m
V1 = 45 x 10^9 Nm^2/C = 45 V
Potential due to Charge 2:
V2 = (9 x 10^9 Nm^2/C^2) * (-3.0 x 10^-6 C) / (0.30m - 0m) [Using the formula V = k * q / r]
V2 = -9 x 10^9 Nm^2/C^2 * 10 C / 0.30m
V2 = -30 x 10^9 Nm^2/C = -30 V
Potential due to Charge 3:
V3 = (9 x 10^9 Nm^2/C^2) * (-4.0 x 10^-6 C) / (0.40m - 0m) [Using the formula V = k * q / r]
V3 = -9 x 10^9 Nm^2/C^2 * 10 C / 0.40m
V3 = -22.5 x 10^9 Nm^2/C = -22.5 V
Adding up the potentials:
Total potential at x=0 = V1 + V2 + V3
= 45 V + (-30 V) + (-22.5 V)
= -7.5 V
Therefore, the potential at x=0 is -7.5 V.
To find the potential at a point due to multiple point charges, you need to calculate the potential due to each charge individually and then sum them up.
The potential at a point due to a point charge can be calculated using the equation:
V = k * q / r
Where:
V is the potential at the point,
k is the Coulomb's constant (9.0 x 10^9 Nm^2/C^2),
q is the charge, and
r is the distance from the charge to the point.
Let's calculate the potential due to each charge individually:
For the +2.0μC charge at x = 20cm, the distance from the charge to x = 0 is 20cm. We convert it to meters: 20cm = 0.2m. The charge is positive, so the potential due to this charge is:
V1 = (9.0 x 10^9 Nm^2/C^2) * (2.0 x 10^-6 C) / 0.2m
V1 = 9.0 x 10^9 * 2.0 x 10^-6 / 0.2
V1 = 9.0 x 10^9 * 1.0 x 10^-6 / 0.2
V1 = 9.0 x 5.0 x 10^3
V1 = 45,000 V
For the -3.0μC charge at x = 30cm, the distance from the charge to x = 0 is 30cm. We convert it to meters: 30cm = 0.3m. The charge is negative, so the potential due to this charge is:
V2 = (9.0 x 10^9 Nm^2/C^2) * (-3.0 x 10^-6 C) / 0.3m
V2 = -9.0 x 10^9 * 3.0 x 10^-6 / 0.3
V2 = -9.0 x 10^9 * 1.0 x 10^-6 / 0.1
V2 = -9.0 x 10^9 * 10.0 x 10^-3
V2 = -90,000 V
For the -4.0μC charge at x = 40cm, the distance from the charge to x = 0 is 40cm. We convert it to meters: 40cm = 0.4m. The charge is negative, so the potential due to this charge is:
V3 = (9.0 x 10^9 Nm^2/C^2) * (-4.0 x 10^-6 C) / 0.4m
V3 = -9.0 x 10^9 * 4.0 x 10^-6 / 0.4
V3 = -9.0 x 10^9 * 1.0 x 10^-6 / 0.1
V3 = -9.0 x 10^9 * 10.0 x 10^-3
V3 = -90,000 V
Now, to find the total potential at x = 0, we sum up the potentials due to each charge:
Total potential = V1 + V2 + V3
= 45,000 V - 90,000 V - 90,000 V
= -135,000 V
Therefore, the potential at x = 0 due to the given point charges is -135,000 volts.
Just use the formula for each point and add 'em up. They're all in a nice straight line, so there are no vector calculations involved.
Take a peek at
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/potpoi.html