(a) The fundamental SI units are meters for length, seconds for time, kilograms for mass, and Coulomb for charge. Use the Coulomb force law for two interacting point charges (F = kq1q2/r2) and the force units you already know from mechanics (N) to find the SI units for Coulomb’s constant k and the constant 0 = 1/4πk. Express your answers using only the four fundamental units. (b) What are the units of the electric field, expressed first using force units (N) and then using only fundamental SI units?
#2
(a) The fundamental SI units are meters for length, seconds for time, kilograms for mass, and
Coulomb for charge. Use the Coulomb force law for two interacting point charges (F = kq1q2/r2)
and the force units you already know from mechanics (N) to find the SI units for Coulomb’s
constant k and the constant 0 = 1/4πk. Express your answers using only the four fundamental
units.
(b) What are the units of the electric field, expressed first using force units (N) and then using only
fundamental SI units?
(c) Visualizing how an electric field varies with location is going to prove very helpful. Using arrows
at several test points in the xy plane - enough points to illustrate the behavior of the fields -
sketch the following electric fields at the test points and briefly describe the behavior of the field
in words. You only need to provide a qualitatively correct plot that is consistent with the vector
function and the description - you don’t need to calculate the vectors although I will show you
how to do it in the solutions. Assume that there is no variation in the z direction nor any z
component to any of the fields.
• E(x, y) = (1N/C) sin(2πx)ˆy
• E(x, y) = (1N/C) sin(2πx)ˆx
• E(r, θ) = −(1N/C)/r2
rˆ
Step by step
Solved in 2 steps with 2 images
