Question

In a circuit with a coil of resistance $2\Omega$, the magnetic flux changes from $2.0Wb$ to $10.0Wb$ in $0.2s$. The charge that flows in the coil during this time is

• A. $5.0C$
• B. $4.0C$
• C. $1.0C$
• D. $0.8C$

Answer 1

The correct option is B

$4.0C$

Step 1: Given data

Resistance in the circuit: $R=2\Omega$

Initial flux: ${\varphi }_1=2Wb$

Final flux: ${\varphi }_2=10Wb$

Time: $t=0.2s$

Step 2: Formula Used

Induced EMF is defined as the rate of change of magnetic flux ${\epsilon }_0=\frac{d\varphi }{dt}$, where $\varphi$ is magnetic flux and $t$ is time.

The current in a circuit is given by $I=\frac{{\epsilon }_0}{R}$, where $R$ is resistance.

The charge flowing through the circuit is given by $q=It$, where $I$ is current and $t$ is time.

Step 3: Calculation

Calculate the electric potential by dividing the change in magnetic flux by time.

$\begin{array}{rcl}{\epsilon }_0& =& \frac{d\varphi }{dt}\\ & =& \frac{{\varphi }_2-{\varphi }_2}{0.2}\\ & =& \frac{10-2}{2}\times 10\\ & =& 40V\end{array}$

Calculate the current by dividing the potential by resistance.

$\begin{array}{rcl}I& =& \frac{{\epsilon }_0}{R}\\ & =& \frac{40}{2}\\ & =& 20A\end{array}$

Calculate the charge by multiplying the current by time.

$\begin{array}{rcl}q& =& It\\ & =& 20A\times 0.2s\\ & =& 4C\end{array}$

Hence, the charge flowing is $4C$.