An electron(charge `= 1.6 xx 10^(19)` coulomb) is moving in a circle of radius `5.1 xx 10^(11) m` at a freqnecy of ` 6.8 xx 10^(15)` revolution/sec. The equivalent current is approximately

Options

A. `5.1 xx 10^(-3)` amp
B. `6.8 xx 10^(-3)` amp
C. `1.1 xx 10^(-3)` amp
D. `2.2 xx 10^(-3)` amo

Answer

To find the equivalent current generated by an electron moving in a circular path, we can use the formula for current (I) in terms of charge (q) and time period (T). The steps are as follows:

### Step 1: Understand the relationship between current, charge, and time
The current (I) is defined as the charge (q) passing through a point in a circuit per unit time (T). Mathematically, this can be expressed as:
\[ I = \frac{q}{T} \]

### Step 2: Determine the time period (T)
The frequency (f) of the electron's revolution is given as \( 6.8 \times 10^{15} \) revolutions per second. The time period (T) is the reciprocal of frequency:
\[ T = \frac{1}{f} \]
Substituting the value of frequency:
\[ T = \frac{1}{6.8 \times 10^{15}} \]

### Step 3: Calculate the time period (T)
Calculating the time period:
\[ T = \frac{1}{6.8 \times 10^{15}} \approx 1.47 \times 10^{-16} \text{ seconds} \]

### Step 4: Substitute the values into the current formula
Now we can substitute the charge of the electron and the time period into the current formula. The charge of the electron (q) is given as \( 1.6 \times 10^{-19} \) coulombs:
\[ I = \frac{1.6 \times 10^{-19}}{1.47 \times 10^{-16}} \]

### Step 5: Calculate the current (I)
Now, performing the division:
\[ I \approx 1.09 \times 10^{-3} \text{ amperes} \]

### Step 6: Round off the answer
Rounding off to two significant figures, we get:
\[ I \approx 1.1 \times 10^{-3} \text{ A} \]

Thus, the equivalent current is approximately \( 1.1 \times 10^{-3} \) amperes.

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