Question

An electron moves in a circle of radius of $1.0\mathrm{cm}$ with a constant speed of $4.0106\mathrm{m}/\mathrm{s}$, electric current at a point on the circle will be: ($e=1.6\times {10}^{-19}\mathrm{C}$)

Answer 1

Step 1: Given data

Radius of circle, $r=1.0\mathrm{cm}=0.01\mathrm{m}$

Speed of the electron, $s=4.0106\mathrm{m}/\mathrm{s}$

Charge of the electron, $e=1.6\times {10}^{-19}\mathrm{C}$

Step 2: Formulas used

Circumference of a circle, $\mathrm{C}=2\mathrm{\pi r}$, where $r$ is the radius of the circle.

Speed, $s=\frac{d}{t}$, where $d$ is the distance traveled and $t$is the time taken.

Current, $\mathrm{I}=\frac{Q}{t}$, where $Q$ is the charge passing through a point and $t$ is the time taken for the charges to pass through the point.

Step 3: Calculate current

From the formula for the circumference of a circle, we can find the distance traveled by the electron. Thus, the distance traveled by it is,

$\begin{array}{rcl}d& =& 2\mathrm{\pi }\times 0.01\\ \therefore d& \approx & 0.063\mathrm{m}\end{array}$

Substituting the values for the respective terms in the formula for speed, we get that the time taken by the electron to complete one revolution in the circle is,

$t=\frac{d}{s}=\frac{0.063}{4.0106}\approx 0.015\mathrm{s}$

From the formula for calculating current, we get that,

$\mathrm{I}=\frac{-1.6\times {10}^{-19}}{0.015}=-1.067\times {10}^{21}\mathrm{A}$

Therefore, the current at a point on the circle is $-1.067\times {10}^{21}\mathrm{A}$.