The thin plastic rod has length L and linear charge density...

The thin plastic rod has length L and linear charge density $\lambda = c \times x$, where c is a constant. With V=0 at infinity, a. Find electric potential at point $P_1$ on the x-axis, at a distance d from one end. b. Find electric potential at point $P_2$ on the y-axis, at y=D. c. Find the electric field component $E_y$ at $P_2$ using the result of (b). d. Explain why you cannot find the field component $E_x$ at $P_2$ using the result of (b).

Transcript

00:01 In this question, we have a uniformly charged rod placed along the x -axis.

00:06 It has length out.

00:08 Want to find the electric fuel along at the point along y -axis, a d distance away from the origin.

00:19 So to do this question, there are two parts in this question.

00:23 First, to find a fuel at distance d along the y -axis.

00:29 And then the second part is to take the consider d much much larger than l and find out what happened to the components.

00:40 Okay, so to do this question, we have a continuous charge distribution, so we need to do integration to find our ex and ey, the x and y components.

00:54 So first we consider here there's a dq, which is lambda dx.

00:59 Then this is distance x and so at this point it will insert it will generate an issue that is along this direction d e, so it has the horizontal component and vertical component okay d e y and d x okay so we'll be using this angle which is also this angle data here and then this distance is using an agarist theorem square root of x squared plus d square okay so um we using uh de equals to k dq over r square okay and then from the diagram d .ex is d .e.

02:06 Cossite data and then d .e .y is d .e.

02:13 Sight data.

02:14 Okay.

02:15 Here i'm just finding magnitude.

02:18 The direction has already been indicated on the diagram.

02:22 But later, when we need to indicate the direction, we will indicate the side.

02:27 Okay and so we need cosine data cossite data is x over square root of x squared plus d square and then side data is d over square of x squared plus d square okay the integration limits x is from zero to l okay okay now you'll find x first.

03:09 X is integral of the x, cosine theta.

03:15 So you'll substitute.

03:17 There's one thing i've got to do.

03:19 Lambda is q over l.

03:21 Okay, so integral of k, the q is lambda d x, and q over l, the x, k, divide by square root of...

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