Two charge of +40 micro coulomb are separated by distance 0.4m determine potential at mid point of them the dielectric constant of medium is2
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To determine the potential at the midpoint between the two charges, we can use the formula for electric potential:
V = k * (q1/r1 + q2/r2)
Where:
- V is the electric potential
- k is the electrostatic constant (k = 9 × 10^9 Nm²/C²)
- q1 and q2 are the charges (in Coulombs)
- r1 and r2 are the distances from the charges to the point where the potential is measured (in meters)
In this case, both charges are equal to +40 microCoulomb (40 × 10^(-6) C), and the distance from each charge to the midpoint is 0.4 m.
Let's substitute these values into the formula:
V = (9 × 10^9 Nm²/C²) * (40 × 10^(-6) C / 0.4 m + 40 × 10^(-6) C / 0.4 m)
V = (9 × 10^9 Nm²/C²) * (0.1 C/m + 0.1 C/m)
V = (9 × 10^9 Nm²/C²) * (0.2 C/m)
V = 1.8 × 10^9 Nm²/C
Now, since the dielectric constant (ε) of the medium is given as 2, we need to multiply the potential by ε:
V = (1.8 × 10^9 Nm²/C) * 2
V = 3.6 × 10^9 Nm²/C
Therefore, the potential at the midpoint between the charges is 3.6 × 10^9 Nm²/C.
To determine the potential at the midpoint between two charges, we can use the formula for electric potential due to a point charge:
V = k * Q / r
Where:
V is the electric potential
k is the electrostatic constant (k = 9 x 10^9 Nm^2/C^2)
Q is the charge
r is the distance between the charge and the point where we want to find the potential
In this case, we have two charges, each with a value of +40 microcoulombs (40 x 10^-6 C). The distance between them is 0.4 m.
Step 1: Calculate the individual potentials at the midpoint for each charge.
The distance between each charge and the midpoint is half of the total distance between the charges. So, the distance between each charge and the midpoint is 0.4 m / 2 = 0.2 m.
For each charge:
Q = 40 microcoulombs = 40 x 10^-6 C
r = 0.2 m
Applying the formula, we get:
V1 = k * Q / r
V1 = (9 x 10^9 Nm^2/C^2) * (40 x 10^-6 C) / 0.2 m
Step 2: Calculate the total potential at the midpoint.
Since the two charges are of the same magnitude, the total potential at the midpoint is the sum of the potentials of each charge.
V_total = V1 + V2
Step 3: Determine the dielectric constant (k) of the medium.
In this case, the dielectric constant of the medium is given as 2.
Step 4: Calculate the final potential at the midpoint.
The formula for the potential due to charged particles in a dielectric medium is:
V_final = V_total / k
Substituting the values, we get:
V_final = (V1 + V2) / k
After calculating V_final, you will find the potential at the midpoint between the two charges in the given dielectric medium.