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Physics 102 Lecture 6

Physics 102 Lecture 6 - It is a hyperbola VB is for the...

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Unformatted text preview: It is a hyperbola VB is for the potential outside the sphere parabolic joins smoothly with VB The curve for VD is for the potential inside the sphere V for a Uniformly Charged Sphere, Graph Continuous Charge Distributions Electric Potential for a Continuous Charge Distribution The potential at some point due to this charge element is Treat it as a point charge Consider a small charge element dq Electric Potential for a Continuous Charge Distribution – alt. V for a Continuous Charge Distribution, cont V for continuous charge distribution For r < R, For r > R, A solid sphere of radius R and total charge Q V for a Uniformly Charged Sphere Charged Conductors V Due to a Charged Conductor This value for V uses the reference of V = 0 when P is infinitely far away from the charge distributions For V, you need to integrate to include the contributions from all the elements V for a Continuous Charge Distribution, cont V Due to a Charged Conductor is always perpendicular to the displacement Then, Therefore, the potential difference between A and B on the surface is also zero Calculate field The ring has a radius a and a total charge Q P on the perpendicular central axis of the uniformly charged ring V for a Uniformly Charged Ring Thus, the surface of any charged conductor in electrostatic equilibrium is an equipotential surface Because E is zero inside the conductor, V is constant inside the conductor and equal to the value at the surface V = 0 between any two points on the surface V is constant on the surface of a charged conductor in equilibrium V Due to a Charged Conductor, cont where Potential from the infinitesimal ring V for a Uniformly Charged Disk Therefore, a cavity surrounded by conducting walls is a field-free region as long as no charges are inside the cavity E inside does not depend on the charge distribution on the outside surface of the conductor For all paths between A and B, Cavity in a Conductor, cont The effect of a charge on the space surrounding it: The charge sets up a vector E which is related to the force The charge sets up a scalar V which is related to the energy V is a function of 1/r E is a function of 1/r2 E Compared to V Then, E is large near the convex points having small radii of curvature and reaches very high values at sharp points And low where the radius of curvature is large Charge density is high where the radius of curvature is small Irregularly Shaped Objects Why? E inside the conductor must be zero Given an arbitrarily shaped cavity inside a conductor and that no charges inside the cavity: Cavity in a Conductor ...
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