Question

an electron moves in a circle of radius 10 centimetre with a constant speed 5.0*10^6 m/s. Find the current at a point on circle.

Answer 1

Concept:

Electric Current : The rate of flow of charge is called electric current.

                                 Electric Current = Charge/Time

                                             I = q/t

Given:

Radius of circle, r = 10 cm = 10×$10^{-2}$ m = 0.1 m

Speed of electron, v = 5.0 × $10^{6}$ m/s

Electronic charge, q = e = 1.6 × $10^{-19}$ C

Find:

Current (I) at a point on the circle.

Solution:

As we know,

                            Current, I = Charge (q)/Time(t)

                                  $I = \frac{q}{t}$      ----------- (i)

And, Speed = Distance/Time

            $v = \frac{s}{t}$                    ----------- (ii)

The electron is moving in a circle, therefore,

s= $2\pi r$ (Circumference of the circle)

Now the equation (ii) becomes,

                                        $v = \frac{2\pi r}{t}$

                                         $t = \frac{2\pi r}{v}$

Putting the value of t in equation (i), we get

$I = \frac{qv}{2\pi r}$

$I = \frac{(1.6 X 10^{-19})(5.0X10^{6}) }{2(3.14)(0.1)}$

$I = \frac{8X10^{-13} }{0.628}$

$I = 12.74 X 10^{-13} A = 1.274 X 10^{-12} A$

Answer:

The current at a point on the circle is 1.274 × $10^{-12}$ A.

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