The electric potential at a position located a distance of 20.1 mm from a positive point charge of 6.50×10-9C and 12.1 mm from a second point charge is 1.26 kV. Calculate the value of the second charge.

Question

The electric potential at a position located a distance of 20.1 mm from a positive point charge of 6.50×10-9C and 12.1 mm from a second point charge is 1.26 kV. Calculate the value of the second charge.

Answer 1

potential is the scalar sum...

1.26E3=k6.5E-9/.0201 + kQ/.0121

solve for Q

Answer 2

To find the value of the second charge, 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 Coulomb's constant (8.99 x 10^9 N m^2/C^2),
q is the charge,
and r is the distance from the charge.

For the first point charge:
q1 = 6.50 x 10^-9 C
r1 = 20.1 mm = 20.1 x 10^-3 m

For the second point charge:
q2 is the unknown charge,
r2 = 12.1 mm = 12.1 x 10^-3 m

The total electric potential (V) at the given position is the sum of the electric potentials due to each point charge:

V_total = V1 + V2

We know the value of the total electric potential V_total = 1.26 kV = 1.26 x 10^3 V (since 1 kV = 1000 V).

Now, we can use the formula to find the electric potential due to each point charge:

V1 = k * q1 / r1

V2 = k * q2 / r2

Substituting the values we have:

1.26 x 10^3 V = (8.99 x 10^9 N m^2/C^2) * (6.50 x 10^-9 C) / (20.1 x 10^-3 m) + (8.99 x 10^9 N m^2/C^2) * q2 / (12.1 x 10^-3 m)

Now, let's solve for q2:

1.26 x 10^3 V = (8.99 x 10^9 N m^2/C^2) * (6.50 x 10^-9 C) / (20.1 x 10^-3 m) + (8.99 x 10^9 N m^2/C^2) * q2 / (12.1 x 10^-3 m)

Multiply both sides of the equation by (12.1 x 10^-3 m) to remove the denominator on the right side:

(1.26 x 10^3 V) * (12.1 x 10^-3 m) = (8.99 x 10^9 N m^2/C^2) * (6.50 x 10^-9 C) + (8.99 x 10^9 N m^2/C^2) * q2

12.146 x 10^-3 V m = (8.99 x 10^9 N m^2/C^2) * (6.50 x 10^-9 C) + (8.99 x 10^9 N m^2/C^2) * q2

Now, isolate q2 by subtracting (8.99 x 10^9 N m^2/C^2) * (6.50 x 10^-9 C) from both sides:

12.146 x 10^-3 V m - (8.99 x 10^9 N m^2/C^2) * (6.50 x 10^-9 C) = (8.99 x 10^9 N m^2/C^2) * q2

Now, divide both sides by (8.99 x 10^9 N m^2/C^2) to solve for q2:

q2 = [12.146 x 10^-3 V m - (8.99 x 10^9 N m^2/C^2) * (6.50 x 10^-9 C)] / (8.99 x 10^9 N m^2/C^2)

Plug in the values and calculate q2.