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# The distance between the wires of electric mains is $12 \mathrm{cm}$ . These wires experience 4 mgwt per unit length. The value of current flowing in each wire will be, if they carry current in the same direction,(A) 4.85 A(B) Zero(C) $4.85\times {{10}^{-2}}A$ (D) $85\times {{10}^{-4}}A$

Last updated date: 09th Aug 2024
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Hint
We know that electric current is the movement of electrons through a wire. Electric current is measured in amperes (amps) and refers to the number of charges that move through the wire per second. Current is usually denoted by the symbol I. Ohm's law relates the current flowing through a conductor to the voltage V and resistance R; that is, V = IR. An alternative statement of Ohm's law is I = V/R. The direction of an electric current is by convention the direction in which a positive charge would move. Thus, the current in the external circuit is directed away from the positive terminal and toward the negative terminal of the battery. Based on this concept we have to solve this question

We know that,
$\dfrac{\mu_{0} I_{1} I_{2}}{2 \pi r}=m g$
From the given equation, we can equate the electromagnetic force and the physical force.
This will help us find out the current value and the direction of flow.
As we have force $= 4$mgwt per unit length
Force per unit length $= 4 \times 9.8 \times 10^{-6} \,N$
and $I_1 = I_2 = I$
as we know that force is given by -
$\dfrac{F}{l} = \dfrac {\mu_0 I_1 I_2}{2 \pi r}$
Here, $\mu_0 = 4\pi \times 10^{-7}$
distance $r = 12 cm = 12 \times 10^{-2}\,m$
$\therefore \dfrac{4 \pi \times 10^{-7} \times I \times I}{2 \pi \times 12 \times 10^{-2}} = 4 \times 10^{-6} \times 9.8$
$\Rightarrow {I^2} = 24 \times 0.98$,
$\Rightarrow I=4.85 \mathrm{A}$ .

Therefore, the correct answer is Option (A).

Note
It is known that mains electricity is the general-purpose alternating-current (AC) electric power supply. It is the form of electrical power that is delivered to homes and businesses. Large transformers are used to run transmission lines at high voltages in order to keep losses to a minimum. But high voltage is dangerous, particularly to life, so bringing it into a house would not be an acceptable risk. DC arcs do not "quench" as easily because voltage does not go through zero. A.C. is said to be four to five times more dangerous than D.C. For one thing, A.C. causes more severe muscular contractions. For another, it stimulates sweating, which lowers the skin resistance. The frequency of the AC has a lot to do with the effect on the human body.