Acceleration of Point Charge Due to Two Other Point Charges
Example
A negative test charge sits 1.4 m away from the middle point between a pair of positive charges. The positive charges are separated by 1.0 m and each have a charge of 2.0 mc.
What is the electric field vector at the position of the negative test charge?
in simple steps
1. Calculate the electric field contribution from each positive charge separately using the formula:
E = k * (q / r^2)
where:
- E is the magnitude of the electric field
- k is the Coulomb's constant, approximately 9.0 x 10^9 Nm^2/C^2
- q is the charge of each positive charge, 2.0 mc
- r is the distance from the positive charge to the negative test charge, which is 1.4 m for this example
For each positive charge, the electric field at the position of the negative test charge is:
E1 = 9.0 x 10^9 Nm^2/C^2 * (2.0 x 10^-6 C) / (1.4 m)^2
= (2.57 x 10^6 N/C) / (1.96 m^2)
= 1.31 x 10^6 N/C
E2 = 9.0 x 10^9 Nm^2/C^2 * (2.0 x 10^-6 C) / (1.4 m)^2
= (2.57 x 10^6 N/C) / (1.96 m^2)
= 1.31 x 10^6 N/C
2. Calculate the net electric field vector at the position of the negative test charge by summing the contributions from the two positive charges:
Electric field at position of negative charge: E_net = E1 + E2
= 1.31 x 10^6 N/C + 1.31 x 10^6 N/C
= 2.62 x 10^6 N/C
3. The direction of the electric field vector at the position of the negative test charge can be determined based on the charges of the positive charges. Since the test charge is negative and the positive charges are positive, the electric field acts away from the positive charges and towards the negative test charge.
Therefore, the electric field vector at the position of the negative test charge is:
E_net = 2.62 x 10^6 N/C, pointing towards the negative test charge.
To find the electric field vector at the position of the negative test charge, you can follow these steps:
Step 1: Calculate the electric field contribution from each positive charge separately.
- Start with one of the positive charges. Let's call it Q1.
- Use the equation for electric field due to a point charge:
E1 = (k * Q1) / r1^2
where k is the Coulomb's constant (9.0 x 10^9 N m^2/C^2), Q1 is the charge of the positive charge, and r1 is the distance from the negative test charge to the positive charge (1.4 m in this case).
- Calculate E1 using the given values.
Step 2: Calculate the electric field contribution from the other positive charge separately.
- Repeat Step 1 for the other positive charge. Let's call it Q2.
- The distance from the negative test charge to this positive charge is the distance from the negative test charge to the middle point between the positive charges, which is 1.0 m.
Step 3: Find the net electric field vector.
- Since the electric field is a vector quantity, you need to consider both the magnitude and direction of the electric field contributions from each positive charge.
- To find the net electric field vector, you can use the principle of superposition. Simply add the electric field vectors from each positive charge.
- If both electric field vectors have the same direction, you can add their magnitudes together.
- If the electric field vectors have different directions, subtract the magnitude of one from the magnitude of the other and use the direction of the greater magnitude.
Step 4: Write down the final result.
- Write down the magnitude and direction of the net electric field vector at the position of the negative test charge.
To find the electric field vector at the position of the negative test charge, you can follow these steps:
1. Start by calculating the electric fields generated by each of the positive charges individually.
- Use Coulomb's Law to calculate the magnitude of the electric fields: E = k * (|q| / r^2), where k is the electrostatic constant (9 x 10^9 N*m^2/C^2), |q| is the magnitude of the charge, and r is the distance between the charges.
- In this case, the magnitude of the charge for each positive charge is 2.0 mc (microcoulombs) or 2.0 x 10^-6 C, and the distance between the positive charges is 1.0 m.
2. Next, calculate the vector direction of each electric field.
- The electric fields generated by positive charges are radial, meaning they point away from each positive charge.
- Determine the direction by considering the position of the negative test charge relative to each positive charge.
3. Once you have the magnitude and direction of each electric field, you can find the net electric field at the position of the negative test charge by vector addition.
- Since the electric fields are vectors, add them together using vector addition.
- If the electric fields have the same direction, simply add their magnitudes.
- If the electric fields have opposite directions, subtract their magnitudes.
4. Finally, you will have the net electric field vector at the position of the negative test charge.