Question 144: Magnetism and Matter

Question

Two long parallel conductors S1 and S2 are separated by a distance 10 cm and carrying currents of 4A and 2A respectively. The conductors are placed along x-axis in X-Y plane. There is a point P located between the conductors (as shown in figure).
A charge particle of 3$$\pi$$ coulomb is passing through the point P with velocity $$\overrightarrow v  = (2\widehat i + 3\widehat j)$$ m/s; where $$\widehat i$$ and $$\widehat j$$ represents unit vector along x & y axis respectively.
The force acting on the charge particle is $$4\pi  	imes {10^{ - 5}}( - x\widehat i + 2\widehat j)$$ N. The value of x is :

Accepted Answer

Field at P is $$ = \left( {{{{\mu _0} 	imes {i_1}} \over {2\pi {r_1}}} - {{{\mu _0}{i_2}} \over {2\pi {r_2}}}} ight)\left( { - \widehat k} ight)$$
$$ =  - \left( {{{{\mu _0}4} \over {2\pi  	imes 0.04}} - {{{\mu _0} 	imes 2} \over {2\pi  	imes 0.06}}} ight)\widehat k =  - {{{\mu _0} 	imes 200} \over {6\pi }}\widehat k$$
So, force $$\overrightarrow F  = q\overrightarrow v  	imes \overrightarrow B $$
$$ = 3\pi \left( {2\widehat i + 3\widehat j} ight) 	imes \left( { - \left( {{{{\mu _0} 	imes 200} \over {6\pi }}\widehat k} ight)} ight)$$
$$ = 3\pi \left( {{{200{\mu _0}} \over {3\pi }}\widehat j - {{100{\mu _0}} \over \pi }\widehat i} ight)$$
$$ = 200{\mu _0}\widehat j - 300{\mu _0}\widehat i$$
$$ = 4\pi  	imes {10^{ - 5}}(2\widehat j - 3\widehat i)$$
So, $$x = 3$$

Answer

2

Answer

1

Answer

3

Answer

$$-$$3

Magnetism and Matter

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