PHYS 208 Lecture 3

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Note similarities in Law of Universal gravity and Coulomb's Law for electric force:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle F_c = k\frac{q_1q_2}{r^2} \quad \quad F_g = G\frac{m_1m_2}{r^2}}

Electric Fields

We've used fields before in mapping Gravitational Fields: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle g = \frac{F_g}{m}}

Measured in Newtons per Coulomb [N/C].

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \vec{E}_\mathrm{pt\ charge} = k\frac{q}{r^2}\hat{r}}

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \vec{F} = q\vec{E}}

• electric field of a positive charge points away from it
• electric field of a negative charge points toward it

In a system of charges, the net electric field is the vector sum of the individual fields for each charge:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \vec{E} = \sum_{i=1}^n k\frac{q_i}{{r_i}^2}\hat{r}_i = \vec{E}_1 + \vec{E}_2 + \dots + \vec{E}_n}

Continuous Point distributions

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \vec{E} = \int k\frac{\mathrm{d}q}{r^2}\hat{r}}

Common Integration Point Charges

• Linear charge distribution: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathrm{d}q = \lambda \mathrm{d}l}
• Surface charge distribution: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathrm{d}q = \sigma \mathrm{d}A}
• Volume charge distribution: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathrm{d}q = \rho \mathrm{d}V}