Two charges 5*10^-8 and -3*10^-8 C are located 16cm apart in air. At
what point on the line joining the two charges is the total electric potential zero? Take the potential at infinity to be zero
put the +5 at x = 0 and the -3 at x = d
at some point beyond d the work done to pull a charge in from x = oo is zero, the +5 pulling one way and the -3 the other way. The potential is proportional to charge *1/distance
total work = c * 5/x - c *3/(x-d)
5/x = 3/(x-d)
5x-5d = 3 x
2 x = 5 d
d = 16 cm
so
x = (5/2)(16) = 40 cm
come closer and the -3 wins
go way far away and it looks like charge of +2 at zero :)
To find the point on the line between the two charges where the total electric potential is zero, we can use the principle of superposition.
The electric potential at a point due to a single charge is given by the equation:
V = k*q / r,
where V is the electric potential, k is the electrostatic constant (9 x 10^9 Nm^2/C^2), q is the charge, and r is the distance from the point to the charge.
Let's consider a point P on the line between the charges. The distance from the positive charge (q1 = 5 x 10^-8 C) to the point P is x and the distance from the negative charge (q2 = -3 x 10^-8 C) to point P is (16 - x) cm.
The electric potential at point P due to the positive charge is given by:
V1 = k*q1 / x.
The electric potential at point P due to the negative charge is given by:
V2 = k*q2 / (16 - x).
According to the principle of superposition, the total electric potential at point P is the sum of V1 and V2:
V_total = V1 + V2.
Since we want the total electric potential to be zero, we solve the equation:
V1 + V2 = 0.
Substituting the values of V1 and V2, we have:
k*q1 / x + k*q2 / (16 - x) = 0.
Substituting the given values:
(9 x 10^9 Nm^2/C^2) * (5 x 10^-8 C) / x + (9 x 10^9 Nm^2/C^2) * (-3 x 10^-8 C) / (16 - x) = 0.
Now, we can solve this equation to find the value of x, which represents the distance from the positive charge to the point where the total electric potential is zero.
To find the point on the line joining the two charges where the total electric potential is zero, we need to use the concept of electric potential due to point charges.
The electric potential due to a point charge is given by the equation:
V = k * q / r
where V is the electric potential, k is the electrostatic constant (9 x 10^9 Nm^2/C^2), q is the charge, and r is the distance from the charge.
Let's call the distance from the positive charge to the point on the line x. Therefore, the distance from the negative charge to the same point is (16 cm - x) or (0.16 m - x).
The electric potential at that point due to the positive charge is given by:
V1 = k * q1 / x
The electric potential at that point due to the negative charge is given by:
V2 = k * q2 / (0.16 - x)
To find the point where the total electric potential is zero, we need to add the electric potentials due to the two charges and set the sum equal to zero:
V1 + V2 = 0
Substituting the values, we get:
k * q1 / x + k * q2 / (0.16 - x) = 0
Now, we can rearrange the equation to solve for x:
k * q1 / x = -k * q2 / (0.16 - x)
Cross-multiplying, we have:
q1 * (0.16 - x) = -q2 * x
Expanding the equation, we get:
0.16 * q1 - q1 * x = -q2 * x
Rearranging the equation, we get:
0.16 * q1 = (q1 - q2) * x
Dividing both sides by (q1 - q2), we get:
x = (0.16 * q1) / (q1 - q2)
Plugging in the values of q1 (-5 x 10^-8 C) and q2 (-3 x 10^-8 C), we have:
x = (0.16 * (-5 x 10^-8)) / ((-5 x 10^-8) - (-3 x 10^-8))
Simplifying the equation, we get:
x = -0.8 cm
Therefore, the total electric potential is zero at a point 0.8 cm from the positive charge, towards the negative charge.