Five very long, straight insulated wires are closely bound together to form a small cable. Currents carried by the wires are : $${I_1} = 20\,A,{I_2} = - 6\,A,{I_3} = 12\,A,{I_4} = - 7\,A,{I_5} = 18\,A.$$ (Negative currents are opposite in direction to the positive). The magnetic field induction at a distance of $$10\,cm$$ from the cable is
A.
$$5\,\mu T$$
B.
$$15\,\mu T$$
C.
$$74\,\mu T$$
D.
$$128\,\mu T$$
Answer :
$$74\,\mu T$$
Solution :
Net current is $$\left( {20 - 6 + 12 - 7 + 18} \right)A,\,{\text{i}}{\text{.e}}{\text{.,}}\,37\,A$$
$$\eqalign{
& r = \frac{{10}}{{100}}m = \frac{1}{{10}}m \cr
& B = \frac{{{\mu _0}I}}{{2\pi r}} = \frac{{4\pi \times {{10}^{ - 7}} \times 37 \times 10}}{{2\pi \times 1}} = 74 \times {10^{ - 6}}T \cr
& = 74\,\mu T. \cr} $$
Releted MCQ Question on Electrostatics and Magnetism >> Magnetic Effect of Current
Releted Question 1
A conducting circular loop of radius $$r$$ carries a constant current $$i.$$ It is placed in a uniform magnetic field $${{\vec B}_0}$$ such that $${{\vec B}_0}$$ is perpendicular to the plane of the loop. The magnetic force acting on the loop is
A battery is connected between two points $$A$$ and $$B$$ on the circumference of a uniform conducting ring of radius $$r$$ and resistance $$R.$$ One of the arcs $$AB$$ of the ring subtends an angle $$\theta $$ at the centre. The value of the magnetic induction at the centre due to the current in the ring is
A.
proportional to $$2\left( {{{180}^ \circ } - \theta } \right)$$
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