An infinite thread of charge density lamda lies along Z axis. The potential difference between the points A(4,3,4) and B (3,4,0)is?
To find the potential difference between points A(4,3,4) and B(3,4,0) due to an infinite thread of charge density λ along the Z-axis, we can use the concept of the electric potential.
The formula for the electric potential due to an infinitely long charged line with charge density λ at a point P located at distance r from the line is given by:
V = (λ / (2πε₀)) * ln(r / a)
Where:
V is the electric potential
λ is the charge density
ε₀ is the permittivity of free space (8.85 x 10⁻¹² F/m)
ln is the natural logarithm function
r is the distance between the point P and the line
a is a constant representing the distance between the point on the line and the origin
In this case, the points A(4,3,4) and B(3,4,0) are not on the Z-axis but have different x, y, and z coordinates. We need to calculate the potential difference between these two points.
Step 1: Calculate the distance between points A and B.
r = √((x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²)
= √((3 - 4)² + (4 - 3)² + (0 - 4)²)
= √((-1)² + 1² + (-4)²)
= √(1 + 1 + 16)
= √18
= 3√2
Step 2: Calculate the potential difference between points A and B.
V(A) = (λ / (2πε₀)) * ln(r / a)
V(B) = (λ / (2πε₀)) * ln(r / a)
The potential difference (ΔV) between points A and B is given by:
ΔV = V(A) - V(B)
Now, we have to specify the value of the charge density λ in order to calculate the potential difference.