Point A and B are 0.1m apart. A Point charge of +3.0*10^-9 c is placed at A and a point charge at -1.0*10^-9c B. X is the point on the straight line between A and B where the electric potential is zero. calculate the distance AX
To solve this problem, we need to make use of the concept of electric potential and apply the principles of Coulomb's Law.
The electric potential at a point due to a point charge can be calculated using the formula:
V = k * (q / r)
Where:
- V is the electric potential at the point,
- k is the electrostatic constant (approximately 8.99 × 10^9 Nm^2/C^2),
- q is the magnitude of the point charge, and
- r is the distance between the point charge and the point where potential is being calculated.
In this case, we have a positive charge at Point A (+3.0 × 10^-9 C) and a negative charge at Point B (-1.0 × 10^-9 C). We need to find the point X on the line AB where the electric potential is zero.
At point X, the electric potential due to the positive charge at A should be equal in magnitude and opposite in sign to the electric potential due to the negative charge at B, since their sum should equal zero:
V_A = -V_B
Using the formula V = k * (q / r), we can set up the equation:
k * (q_A / r_AX) = -k * (q_B / r_BX)
Now let's substitute the given values:
8.99 × 10^9 * (3.0 × 10^-9 C / r_AX) = -8.99 × 10^9 * (-1.0 × 10^-9 C / r_BX)
Simplifying the equation:
3.0 / r_AX = 1.0 / r_BX
Now we know that the distance between point A and point B is 0.1m. So the sum of distances r_AX and r_BX must equal 0.1m:
r_AX + r_BX = 0.1
Since we have an equation with two variables (r_AX and r_BX), we can solve it using simultaneous equations. Substituting the relation we found earlier:
3.0 / r_AX = 1.0 / (0.1 - r_AX)
Cross-multiplying:
r_AX = 3.0 * (0.1 - r_AX)
r_AX = 0.3 - 3.0 * r_AX
Simplifying:
4.0 * r_AX = 0.3
r_AX = 0.3 / 4.0
r_AX = 0.075
Therefore, the distance AX is 0.075m.