Question

A magnet is taken towards a conducting ring in such a way that a constant current of $10mA$ is induced in it. The total resistance of the ring is $0.5\Omega$. In$5s,$ the magnetic flux through the ring changes by?

Answer 1

Step 1: Given data:

The constant induced current is given as: $I=10mA$

The total resistance of the ring is given as; $\mathrm{R}=0.5\mathrm{\Omega }$

Time is given as; $t=5s$

Step 2: Formula applied:

According to the principle of magnetic induction,the formula for charge can be given as:

$△q=\frac{△\varphi }{R}$

Where,$△q=$the change in charge

$R=$Resistance

$△\varphi =$Change in flux

The above equation can also be written as:

$$\begin{gathered} i△t=\frac{△\varphi }{R} \\ \because ∆\mathrm{q}=i△t \end{gathered}$$

Where,

$i\mathit{=}$the change in current

$△t\mathit{=}$the change in time

$\Rightarrow △\varphi =i(△t)R$

Step 3: Finding the magnetic flux:

By applying the given data in the above formula we can calculate the change in magnetic flux through the ring as:

$\Rightarrow △\varphi =i(△t)R$

$$\begin{gathered} =\left(10\times {10}^{-3}\right)\left(5\right)\left(0.5\right) \\ =25mWb \end{gathered}$$

Hence, the magnetic flux through the ring changes by $25mWb$.