Nonuniform line of charge, find the electric potential

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SUMMARY

The discussion focuses on calculating the electric potential due to a nonuniform linear charge distribution defined by λ = bx, where b = 25 nC/m², along the x-axis from x = 0 to x = 0.50 m. The electric potential V at the point (0, 0.30 m) is derived using the formula V = ∫[k * dq/r] from x = 0 to x = 0.5 m, where dq = bx * dx and r = √(0.3² + x²). The integration process is essential to determine the electric field at the specified point, as the charge distribution is nonuniform.

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A nonuniform linear charge distribution given by λ = bx, where b is a constant, is located along an x-axis from x = 0 to x = 0.50 m. Suppose that b = 25 nC/m2 and V = 0 at infinity. (b) What is the electric potential at the point y = 0.30 m on the y axis?
E = kq/r^2
V = -Ed
Since there's no charge on the y, I think I would have to find the E-field at that point on y, and then use V = -Ed. But how do I integrate the E-field if it's nonuniform?

And is this what I'm supposed to do?
 
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Potential at any point is given by
V = k*Q/r.
Since charge distribution is nonuniform
V = Intg[k*dq/r] between x = 0 to x = 0.5 m
Now dQ = bx*dx and r = sqrt( 0.3^2 + x^2)
Find the integration.
 

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