A nonuniform linear charge distribution given by $\lambda$(x)= bx,where b is a constant,is distributed along the x axis from x = 0 to x = +L.If b = 40 nC/m² and L = 0.20 m,what is the electric potential (relative to a potential of zero at infinity)at the point y = 2L on the y axis? A)19 V B)17 V C)21 V D)23 V E)14 V

Question

Quizplus · Accepted Answer

The electric potential due to a nonuniform linear charge distribution is given by the following equation:

V(y) = ∫ kλ(x)dx / (y^2 + x^2)^(1/2)

where λ(x) is the linear charge density (in C/m) at distance x from the origin, k is the Coulomb constant (9×10^9 N·m^2/C^2), and y is the distance of the point where the potential is to be calculated from the origin along the y-axis.

In this case, the linear charge density is given by λ(x) = bx = 40x nC/m, where x is in meters.

Therefore, we can write:

V(y) = ∫k(40x/L)dx / (y^2 + x^2)^(1/2)

Integrating from x=0 to x=L, we get:

V(y) = k40/L ∫x/(y^2 + x^2)^(1/2) dx [from x=0 to x=L]

V(y) = k40/L [(y^2 + L^2)^(1/2) - y]

Substituting the given values, we get:

V(y) = (9×10^9 N·m^2/C^2) × 40 nC/m × 0.20 m / [(2×0.20 m)^2 + 0.40 m^2]^(1/2)

V(y) = 17 V

Therefore, the electric potential at the point y = 2L on the y-axis is 17 V. Hence, the correct answer is B.

A Nonuniform Linear Charge Distribution Given By λ\lambdaλ (X)= Bx,where B Is a Constant,is Distributed Along the X

A Nonuniform Linear Charge Distribution Given By $\lambda$ (X)= Bx,where B Is a Constant,is Distributed Along the X