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Electricity and Magnetism

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Moderate

Electric Field Dependence on Configuration Size

EANDM-NM67WT

Figure 1 depicts an end-on line of charge - a line of charge of length $l$ in which the field point $P$ lies a distance $x$ from the end of the line of charge and the orientation of the line of charge is parallel to the $\hat{x}$ axis.

Figure 1. Timothy Black. Created for Albert.io. Copyright 2016. All rights reserved.

Figure 2 depicts a transverse line of charge - a line of charge of length $l$ in which the field point $P$ lies a distance $x$ from the center of the line of charge and the orientation of the line of charge is perpendicular to the $\hat{x}$-axis.

Figure 2. Timothy Black. Created for Albert.io. Copyright 2016. All rights reserved.

Figure 3 depicts a ring of charge - a circular line of charge of length $l = 2\pi \rho$ in which the field point $P$ lies a distance $x$ from the center of the ring of charge and the $\hat{x}$ axis is perpendicular to the plane containing the ring of charge.

Figure 3. Timothy Black. Created for Albert.io. Copyright 2016. All rights reserved.

All three lines of charge have the same charge $q = 2 \text{ nC}$ placed upon them and have the same length. $l$.

Figure 4 depicts the magnitude of the electric field as a function of $l$ for the three different lines of charge.

Figure 4. Timothy Black. Created for Albert.io. Copyright 2016. All rights reserved.

All fields are calculated at a field point located a distance $x = 4 \text{ mm}$ from the point $P$ shown in Figures 1, 2, and 3. Note that the vertical axis of this graph uses a logarithmic scale.

The red line corresponds to the field due to

.

The green line corresponds to the field due to

.

The blue line corresponds to the field due to

.