The quantity of charge q (in coulombs) that has passed...

The quantity of charge $q$ (in coulombs) that has passed through a surface of area $2.00 \mathrm{cm}^{2}$ varies with time according to the equation $q=4 t^{9}+5 t+6,$ where $t$ is in seconds. (a) What is the instantancous current through the surface at $t=1.00 \mathrm{s} ?$ (b) What is the value of the current density?

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Key Concepts

Unit Conversion

Unit conversion is crucial in physics to ensure consistency across calculations. For example, converting area from square centimeters to square meters allows for proper use of SI units, which is necessary when calculating physical quantities such as current density.

Current Density

Current density is defined as the current per unit area through which the current is flowing. It provides a measure of how concentrated the current is over a given surface.

Derivative

The derivative represents the instantaneous rate of change of a function with respect to a variable. In this context, taking the derivative of the charge with respect to time gives the instantaneous rate at which charge is flowing, which is the current.

Instantaneous Current

Instantaneous current is the current at a specific moment in time and is calculated by differentiating the time-dependent charge function. It assesses how quickly the charge is changing at a particular instant.

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