Two point charges are 2.00 m apart as shown on the right. The charge of the first object is -1.50 C, while the second object has a charge of +6.85 C. At which point will the electric field vector be zero?
in simple steps
To find the point where the electric field vector is zero, we can use the principle of superposition. According to this principle, the electric field at a point due to multiple charges is the vector sum of the electric fields at that point due to each individual charge.
1. First, let's calculate the electric field at the point P1 (to the right of the -1.50 C charge). The electric field due to the -1.50 C charge can be calculated using Coulomb's law:
E1 = k * q1 / r1^2
where k is the Coulomb's constant (approximately 9 * 10^9 N m^2/C^2), q1 is the charge of the -1.50 C object, and r1 is the distance between the -1.50 C object and the point P1.
2. Next, let's calculate the electric field at the point P2 (to the left of the +6.85 C charge). The electric field due to the +6.85 C charge can be calculated using Coulomb's law:
E2 = k * q2 / r2^2
where q2 is the charge of the +6.85 C object, and r2 is the distance between the +6.85 C object and the point P2.
3. Now, we need to find the point where the electric field vectors cancel each other out. This means that the vector sum of E1 and E2 should be zero:
E1 + E2 = 0
4. Rearranging the equation, we have:
E1 = -E2
5. Substituting the expressions for E1 and E2 from step 1 and step 2 respectively:
k * q1 / r1^2 = -k * q2 / r2^2
6. Simplifying, we have:
q1 / r1^2 = -q2 / r2^2
7. Rearranging the equation, we have:
q1 / q2 = -r1^2 / r2^2
8. Substituting the given values: q1 = -1.50 C, q2 = +6.85 C, r1 = 2.00 m, and r2 = 2.00 m:
-1.50 C / 6.85 C = -4.00 m^2 / 2.00 m^2
9. Simplifying, we have:
-0.2197 ≈ -0.25 ≈ -1/4
10. From step 9, we can conclude that the ratios of distances between the -1.50 C charge and the point P1, and between the +6.85 C charge and the point P2 are in the ratio of 1:2. Therefore, the point where the electric field vector is zero is 1/3 of the way from the -1.50 C charge towards the +6.85 C charge.
So, the electric field vector will be zero at a point 2/3 of the distance from the -1.50 C charge towards the +6.85 C charge.
To find the point where the electric field vector is zero, follow these steps:
Step 1: Calculate the electric field due to the first object at a point located a distance x from the first object.
- Use Coulomb's law formula:
E1 = k * (q1 / r1^2), where
E1 is the electric field due to the first object,
k is the electrostatic constant (8.99 x 10^9 Nm^2/C^2),
q1 is the charge of the first object (-1.50 C),
and r1 is the distance between the first object and the point (x).
Step 2: Calculate the electric field due to the second object at a point located a distance (2.00 - x) from the second object.
- Use Coulomb's law formula again:
E2 = k * (q2 / r2^2), where
E2 is the electric field due to the second object,
q2 is the charge of the second object (+6.85 C),
and r2 is the distance between the second object and the point (2.00 - x).
Step 3: Set the sum of the electric fields to zero.
- Since the electric field is a vector, the total electric field at any point is the vector sum of the individual electric fields.
- Set E1 + E2 = 0 and solve for x.
Step 4: Plug in the values and solve the equation.
Step 5: The value of x obtained is the distance from the first object where the electric field vector is zero.
Note: A negative value of x indicates that the point is to the left of the first object, while a positive value indicates a point to the right.
To find the point where the electric field vector is zero, we need to calculate the electric field at different points between the two charges and determine where it becomes zero.
Here are the steps to find the point:
Step 1: Determine the direction of the electric field created by each point charge.
- The electric field created by a positive charge points away from it, while the electric field created by a negative charge points towards it.
Step 2: Calculate the electric field due to the first charge at a point between the charges.
- Use Coulomb's law to calculate the electric field at the chosen point. The formula is given as:
Electric Field = k * (charge / distance^2)
Where k is the electrostatic constant (9.0 x 10^9 N m^2/C^2), charge is the magnitude of the charge, and distance^2 is the distance between the charge and the point squared.
Step 3: Calculate the electric field due to the second charge at a point between the charges in the opposite direction.
- Use Coulomb's law to calculate the electric field at the chosen point. The formula is the same as in step 2, but the charge will have the opposite sign as the first charge.
Step 4: Add the electric fields from both charges to find the net electric field at the chosen point.
- Since the electric field is a vector quantity, we need to consider both the magnitude and direction of each electric field.
Step 5: Repeat steps 2-4 for different points along the line connecting the two charges.
- Choose different points between the charges to determine how the electric field changes.
Step 6: When the net electric field at a point becomes zero, it means that the electric fields due to the charges cancel each other out.
- Locate the point where the net electric field is zero, which implies that the magnitudes and directions of the electric fields due to the charges balance each other.
Step 7: This point is the location where the electric field vector will be zero between the two charges.