The charges 10micro C and -10 micro C are placed at a point A and B seprated by a distance of 10 cm. Find the electric field on the perpendicular bisector of ab at a distance of 12cm from its middle point.
distance from each = d = sqrt(5^2+12^2) = 13 cm = .13 meter
however we may notice that the component along the bisector will be zero due to the opposite signs of the charges. However that is no true of the component along the direction between charges
E = k q/.13^2 for each
multiply by 5/13 to get component along line
To find the electric field on the perpendicular bisector of AB at a distance of 12 cm from its midpoint, we can calculate the electric field due to each charge and then find their vector sum.
Given:
Charge at point A, q1 = +10 μC
Charge at point B, q2 = -10 μC
Distance between A and B, d = 10 cm
Step 1: Calculate the electric field due to charge q1:
Using Coulomb's law, the electric field due to a point charge is given by:
E1 = k * q1 / r1^2
Here, k is the electrostatic constant, q1 is the charge at point A, and r1 is the distance from the midpoint to point A.
Given:
r1 = 5 cm = 0.05 m (half the distance between A and B)
k = 9 * 10^9 N m^2 / C^2 (Coulomb's constant)
Calculating:
E1 = (9 * 10^9 N m^2 / C^2) * (10 * 10^-6 C) / (0.05 m)^2
Step 2: Calculate the electric field due to charge q2:
Using Coulomb's law, the electric field due to a point charge is given by:
E2 = k * q2 / r2^2
Here, q2 is the charge at point B, and r2 is the distance from the midpoint to point B.
Given:
r2 = 5 cm = 0.05 m (half the distance between A and B)
Calculating:
E2 = (9 * 10^9 N m^2 / C^2) * (-10 * 10^-6 C) / (0.05 m)^2
Step 3: Find the vector sum of E1 and E2:
Since the charges at A and B are equal in magnitude but opposite in sign, the electric fields due to each of them will have the same magnitude but opposite directions. Therefore, we can simply subtract the magnitudes to find the net electric field.
Given:
E1 = 8.1 * 10^6 N/C (calculated in Step 1)
E2 = -8.1 * 10^6 N/C (calculated in Step 2)
Calculating:
E_net = E1 - E2
E_net = 8.1 * 10^6 N/C - (-8.1 * 10^6 N/C)
E_net = 16.2 * 10^6 N/C
E_net = 1.62 * 10^7 N/C
Therefore, the electric field on the perpendicular bisector of AB at a distance of 12 cm from its midpoint is 1.62 * 10^7 N/C.
To find the electric field on the perpendicular bisector of AB, we need to calculate the electric field due to both charges at the given point.
The electric field due to a point charge is given by the formula:
E = (k * Q) / r^2
Where:
E is the electric field,
k is Coulomb's constant (k = 9 × 10^9 Nm^2/C^2),
Q is the charge,
r is the distance from the charge to the point (in meters).
Let's calculate the electric field due to the positive charge (10 µC) first:
Q1 = 10 µC = 10 × 10^-6 C
r1 = distance from the positive charge to the point on the perpendicular bisector (12 cm = 0.12 m)
E1 = (k * Q1) / r1^2
Next, let's calculate the electric field due to the negative charge (-10 µC):
Q2 = -10 µC = -10 × 10^-6 C
r2 = distance from the negative charge to the point on the perpendicular bisector (12 cm = 0.12 m)
E2 = (k * Q2) / r2^2
Since the electric field is a vector quantity, the total electric field on the perpendicular bisector is the vector sum of the electric fields due to each charge. Since the charges are of equal magnitude but opposite sign, the fields will have the same magnitude but opposite directions.
To find the net electric field at a point on the perpendicular bisector, we can add the individual electric field vectors:
E_net = E1 + E2
Now, let's calculate the magnitude and direction of the net electric field.
Magnitude:
E_mag = abs(E_net)
Direction:
If E_net is positive, it points away from both charges on the perpendicular bisector.
If E_net is negative, it points towards both charges on the perpendicular bisector.
Finally, we have the electric field on the perpendicular bisector at a distance of 12 cm from its midpoint.