Question

The electric field intensity produced by the radiation coming from a $100W$ bulb at a distance of $3m$ is $E$. The electric field intensity produced by the radiation coming from$60W$ at the same distance is $\sqrt{\frac{x}{5}}E$. Where the value of $x=$?

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is C

$3$

Step 1: Given data

Power of first bulb$\left(P_1\right)$=$100W$

Distance from the first bulb is $3m$

Electric field intensity coming from $100W$ bulb at a distance of $3m$ is =$E$

Power of the second bulb$\left(P_2\right)=60W$

Electric field intensity produced by the radiation coming from$60W$ at the same distance is $E\text{'}=\sqrt{\frac{x}{5}}E$

Step 2: Formula used

The relation between the intensity of electromagnetic radiation and the electric field is given by the following formula,

$I=c{\epsilon }_{°}{E}^{2}WhereI=intensity,{\epsilon }_{\circ }=Permittivity,E=electricfieldandc=speedoflight$

From the formula, it is clear that the intensity is directly proportional to the square of the electric field. So,

$I\propto E^2$

We know that the $intensity\left(I\right)=\frac{Power\left(P\right)}{Area\left(A\right)}$.

So,

$\frac{P}{A}\propto E^2$…….(1)

Step 3: Compute the value of $x$

According to the problem, the distance is the same therefore $A$ will be the same. So, using equation (1)

$$\begin{gathered} \frac{P_1}{P_2}=\frac{E^2}{E{\text{'}}^2} \\ \sqrt{\frac{P_1}{P_2}}=\frac{E}{E^{\text{'}}} \\ \sqrt{\frac{100}{60}}=\frac{E}{E^{\text{'}}} \\ {E}^{\text{'}}=\sqrt{\frac{3}{5}}E \end{gathered}$$

Comparing $E^{\text{'}}=\sqrt{\frac{3}{5}}E$ with $\sqrt{\frac{x}{5}}E$ we get $x=3$.

Thus the value of $x$ will be $3$.

Hence, option C is the correct answer.