The energy supplied to Kolkata by the state electricity board during an average November week day was 40 GWh. If this energy could be obtained by the conservation of matter, how much mass would have to be annihilated?

Question

A charge of 2 $\mu C$ is placed in an electric field of intensity $ 4 \times 10^3 \, \text{N/C} $. What is the force experienced by the charge?

Answer 1

To solve this question, we need to understand the concept of mass-energy equivalence, as described by Einstein's famous equation:

$E = mc^2$

Where $E$ is the energy, $m$ is the mass, and $c$ is the speed of light in a vacuum, approximately $3 \times 10^8$ m/s.

We are given that the energy supplied is 40 GWh. First, we convert this energy into joules:

Therefore:

$40 \text{ GWh} = 40 \times 10^9 \times 3600 \text{ J}$

Calculating this gives:

$40 \times 10^9 \times 3600 = 144 \times 10^{12} \text{ J}$

Now, using $E = mc^2$, we solve for $m$:

$m = \frac{E}{c^2} = \frac{144 \times 10^{12}}{(3 \times 10^8)^2} \text{ kg}$

This simplifies to:

$m = \frac{144 \times 10^{12}}{9 \times 10^{16}} \text{ kg}$

$m = \frac{144}{9} \times 10^{-4} \text{ kg} = 16 \times 10^{-4} \text{ kg} = 1.6 \times 10^{-3} \text{ kg}$

$1.6 \times 10^{-3} \text{ kg} = 1.6 \text{ g}$

Therefore, the mass that would need to be annihilated to produce 40 GWh of energy is 1.6 g.

The correct answer is: 1.6 g

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