Nonuniform line of charge, find the electric potential

AI Thread Summary
The discussion focuses on calculating the electric potential at a point on the y-axis due to a nonuniform linear charge distribution defined by λ = bx, with b = 25 nC/m² over the interval from x = 0 to x = 0.50 m. To find the electric potential at y = 0.30 m, the electric field E must be determined first, which involves integrating the charge distribution. The potential V is calculated using the formula V = ∫(k * dq/r) from x = 0 to x = 0.5 m, where dq is expressed as bx dx and r is the distance from the charge element to the point of interest. The integration will yield the total electric potential at the specified point. This approach effectively addresses the challenges posed by the nonuniform charge distribution.
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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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