Question

In a magnetic field of 0.05T, the area of a coil changes from 101 cm² to 100 cm² without changing the resistance which is 2 Ω. The amount of charge that flow during this period is

• A. 2.5 x 10^-6 C
• B. 2 x 10^-6 C
• C. 10^-6 C
• D. 8 x 10^-6 C

Answer 1

The correct option is A

2.5 x 10^-6 C

Step1: Given data

Magnetic field, $B=0.05T$

Resistance, $R=2\Omega$

A coil changes from $101c{m}^{2}to100c{m}^2$

Step2: Magnetic flux

1. The total number of magnetic field lines that travel through a closed surface can be defined like this. The overall magnetic field in a particular area is measured by this quantity.
2. The areas that we investigate are of various sizes and orientations in relation to the magnetic field direction.
3. A flux meter is commonly used to measure it. Flux is measured in a variety of units.
4. Weber, abbreviated as Wb in the SI system, is the SI unit.
5. It's an excellent tool for determining the magnetic force on a certain area. It has to do with the chosen region, and we may choose any size and organize it according to the magnetic field.

Step3: Formula for magnetic flux

${\varphi }_B=B.A[where{\varphi }_B=Magneticflux,B=magneticfield,A=Area]$

Step4: Calculating the change in flux

$$\begin{gathered} d\varphi =B.A \\ d\varphi =B.dA \\ d\varphi =(0.05)(101-100)\times {10}^{-4} \\ d\varphi =5\times {10}^{-6}Wb \end{gathered}$$

Step5: Calculate the charge

$$\begin{gathered} dQ=\frac{d\varphi }{R} \\ dQ=\frac{5\times {10}^{-6}}{2} \\ dQ=2.5\times {10}^{-6}C \end{gathered}$$

Hence, option A is the correct answer.