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Chapter 25: Q. 38 (page 711)

A -10.0 nC point charge and a +20.0 nC point charge are 15.0 cm apart on the x-axis. a. What is the electric potential at the point on the x-axis where the electric field is zero? b. What is the magnitude of the electric field at the point on the x-axis, between the charges, where the electric potential is zero?

Short Answer

Expert verified

The electric potential at the x-axis point is 103 V

The magnitude of the electric field at the x-axis point is-5.4×104N.Ci¯

Step by step solution

01

The theory of  electric potential  

As the equation of the electric field of a point is

E=1/(4πε0)q/d2q1=10×10-9CE1=1/(4πε0)[(10×10-9C)/d2]q2=20×10-9Cd=0.15m+dE2=1/(4πε0)[(20×10-9C)/(0.15m+d)2]

As

E1=E2

The electric potential value

0.15m+dd=2d=0.362mV=kq1d+kq2m+dV=103V

02

Definition of The magnitude of the electric field 

As per the figure

V=kq1d+kq20.15m-d

Applying all values in the above equation

d=0.05m

Applying the value of d,

E1=(-36000N.C)i¯E2=(-18000N.C)i¯E1+E2=-5.4×104N.Ci¯

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FIGURE P25.71 shows a thin rod with charge Q that has been bent into a semicircle of radius R. Find an expression for the electric potential at the center.

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