(b) The corresponding electric field lines are found by drawing them perpendicular to the equipotentials. Note bigwins casino login that these fields are consistent with two equal negative charges. The field has a non-zero component along the surface if it was not perpendicular to the equipotential surface. Work would be required to shift a unit test charge in the opposite direction as the component of the field.
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For a point charge, equipotential surfaces are spheres centered on the charge. The equipotential surface concept builds clear links to other JEE topics like Gauss’s law, potential energy of electric dipole, and electrostatic potential and capacitance. Practice visualising and mapping surfaces for all typical configurations. Remember, electric field is always highest where equipotential surfaces are closest together. The surface charge density on a long straight metallic pipe is latex\sigma/latex. These have equipotential lines that are parallel to the plates in the space between and evenly spaced.
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Figure 7.31 shows the electric field and equipotential lines for two equal and opposite charges. Given the electric field lines, the equipotential lines can be drawn simply by making them perpendicular to the electric field lines. Conversely, given the equipotential lines, as in Figure 7.32(a), the electric field lines can be drawn by making them perpendicular to the equipotentials, as in Figure 7.32(b).
An example of this (with sample values) is given in Figure 7.35. We could draw a similar set of equipotential isolines for gravity on the hill shown in Figure 7.2. If the hill has any extent at the same slope, the isolines along that extent would be parallel to each other. Furthermore, in regions of constant slope, the isolines would be evenly spaced. This equation tells us that the distance r from the point charge remains constant for all points on the equipotential surface. In other words, the equipotential surface for a point charge is a sphere centered at the charge, with a radius r given by the above equation.
The equipotential lines around the heart, the thoracic region, and the axis of the heart are useful ways of monitoring the structure and functions of the heart. An electrocardiogram (ECG) measures the small electric signals being generated during the activity of the heart. More about the relationship between electric fields and the heart is discussed in Energy Stored in Capacitors.
