Question 318: Electromagnetic Induction

Question

At what rate a single conductor should cut the magnetic flux so that current of $$1.5 \mathrm{~mA}$$ flows through it when a resistance of $$5 \Omega$$ is connected across its ends?

Accepted Answer

To determine at what rate a single conductor should cut the magnetic flux to produce a current of $$1.5 \mathrm{~mA}$$ when a resistance of $$5 \Omega$$ is connected across its ends, we can use Faraday's law of electromagnetic induction and Ohm's law.
First, let's start with Ohm's law, which states:
$$ V = IR $$
Where:
$$V$$ is the voltage (emf) induced in the conductor
$$I$$ is the current
$$R$$ is the resistance
Given that the current $$I = 1.5 \mathrm{~mA} = 1.5 	imes 10^{-3} \mathrm{~A}$$ and the resistance $$R = 5 \Omega$$, we can substitute these values into Ohm's law to find the induced voltage $$V$$:
$$ V = (1.5 	imes 10^{-3} \mathrm{~A}) 	imes (5 \Omega) $$
$$ V = 7.5 	imes 10^{-3} \mathrm{~V} $$
Next, we use Faraday's law of electromagnetic induction, which states that the induced emf (voltage) in a conductor moving through a magnetic field is equal to the rate of change of magnetic flux linkage:
$$ V = \frac{d\Phi}{dt} $$
Where:
$$V$$ is the induced emf
$$\frac{d\Phi}{dt}$$ is the rate of change of magnetic flux
Given that we have already found $$V = 7.5 	imes 10^{-3} \mathrm{~V}$$, we can substitute this value in to find the rate of change of magnetic flux:
$$ \frac{d\Phi}{dt} = 7.5 	imes 10^{-3} \mathrm{~wb/s} $$
Therefore, the conductor should cut the magnetic flux at a rate of $$7.5 	imes 10^{-3} \frac{\mathrm{wb}}{\mathrm{s}}$$.
The correct option is:
Option D $$7.5 	imes 10^{-3} \frac{\mathrm{wb}}{\mathrm{s}}$$

Answer

$$6 	imes 10^{-3} \frac{\mathrm{wb}}{\mathrm{s}}$$

Answer

$$8 	imes 10^{-3} \frac{\mathrm{wb}}{\mathrm{s}}$$

Answer

$$4 	imes 10^{-4} \frac{\mathrm{wb}}{\mathrm{s}}$$

Answer

$$7.5 	imes 10^{-3} \frac{\mathrm{wb}}{\mathrm{s}}$$

Electromagnetic Induction

At what rate a single conductor should cut the magnetic flux so that current of $1.5 \mathrm{~mA} flows through it when a resistance of 5 \Omega$ is connected across its ends?

Choose the correct answer: