Two point charges of +30μC and -10μC are separated by a distance of 10cm. What is the magnitude of electric field due to these charges at a point midway between them? (k = 9 × 109 N · m2/C2)
The electric field due to these charges at a point midway between them is 60 kN/C.
To find the magnitude of the electric field due to the charges at the point midway between them, we can use the formula for the electric field due to a point charge:
Electric Field (E) = k * (Q / r^2)
Where:
- "E" is the electric field
- "k" is the electrostatic constant (9 × 10^9 N m^2/C^2)
- "Q" is the charge
- "r" is the distance between the charge and the point
In this case, we have two point charges: Q1 = +30μC and Q2 = -10μC. The distance between them is 10cm (0.1m), and we want to find the electric field at the point midway between them.
Step 1: Find the electric field due to Q1:
E1 = k * (Q1 / r^2)
= (9 × 10^9 N m^2/C^2) * (30 × 10^-6 C / (0.05m)^2)
= 540 N/C
Step 2: Find the electric field due to Q2:
E2 = k * (Q2 / r^2)
= (9 × 10^9 N m^2/C^2) * (-10 × 10^-6 C / (0.05m)^2)
= -180 N/C
Step 3: Add the electric field due to each charge to get the total electric field at the midpoint:
E_total = E1 + E2
= 540 N/C - 180 N/C
= 360 N/C
Therefore, the magnitude of the electric field at the point midway between the charges is 360 N/C.
To find the magnitude of the electric field due to two point charges at a point midway between them, we can use the formula for the electric field:
E = (k * q) / r^2
Where:
- E is the electric field
- k is the Coulomb's constant: 9 × 10^9 N · m^2/C^2
- q is the charge of the point charge
- r is the distance between the point charge and the point where the electric field is measured
In this case, we have two charges: +30μC and -10μC. The distance between them is 10cm. The point we are interested in is midway between them, which means the distance to each charge is 5cm.
Let's calculate the electric field due to +30μC at this point first:
q = 30μC = 30 × 10^(-6) C
r = 5cm = 5 × 10^(-2) m
Plugging these values into the formula:
E1 = (k * q) / r^2
E1 = (9 × 10^9 N·m^2/C^2) * (30 × 10^(-6) C) / (5 × 10^(-2) m)^2
Simplifying the equation:
E1 = (9 × 10^9 N·m^2/C^2) * (30 × 10^(-6) C) / (5 × 10^(-2) m)^2
E1 = (9 × 10^9 N·m^2/C^2) * (30 × 10^(-6) C) / (25 × 10^(-4) m^2)
E1 = (270 × 10^3 N·m^2/C) / (25 × 10^(-4) m^2)
E1 = 10.8 × 10^6 N/C
Now, let's calculate the electric field due to -10μC at this point:
q = -10μC = -10 × 10^(-6) C
r = 5cm = 5 × 10^(-2) m
Using the same formula:
E2 = (k * q) / r^2
E2 = (9 × 10^9 N·m^2/C^2) * (-10 × 10^(-6) C) / (5 × 10^(-2) m)^2
Simplifying the equation:
E2 = (9 × 10^9 N·m^2/C^2) * (-10 × 10^(-6) C) / (5 × 10^(-2) m)^2
E2 = (-90 × 10^3 N·m^2/C) / (25 × 10^(-4) m^2)
E2 = -3.6 × 10^6 N/C
Finally, to find the total electric field magnitude at the point midway between the charges, we need to add the magnitudes of the electric fields due to each charge:
E_total = |E1 + E2|
E_total = |10.8 × 10^6 N/C + -3.6 × 10^6 N/C|
Taking the absolute value:
E_total = 14.4 × 10^6 N/C
Therefore, the magnitude of the electric field due to these charges at a point midway between them is 14.4 × 10^6 N/C.