Question 218: Magnetism and Matter

Question

A Helmholtz coil has a pair of loops, each with $$N$$ turns and radius $$R$$. They are placed coaxially at distance $$R$$ and the same current $${\rm I}$$ flows through the loops in the same direction. $$P,$$ midway between the centers $$A$$ and $$C$$, is given by [Refer to figure given below] :

Accepted Answer

P is the mid-point of line AC. A and C are the  center of the two circle of each radius R.
Current flows through loop A and B are  in same direction,  So the magnetic field will also be in the same direction. Magnitude of magnetic field at paint  P
= magnitude of magnetic field due to A and  B at paint P.
= 2 $$\left[ {{{{\mu _0}NI\,{R^2}} \over {2{{\left( {{R^2} + {{{R^2}} \over 4}} \right)}^{{3 \over 2}}}}}} \right]$$
$$=$$ $${{{\mu _0}\,NI{R^2}} \over {{{{5^{{3 \over 2}}}{R^3}} \over 8}}}$$
= $${{8\,{\mu _0}NI} \over {{5^{{3 \over 2}}}\,R}}$$

Answer

$${{8N{\mu _0}{\rm I}} \over {{5^{1/2}}R}}$$

Answer

$${{8N{\mu _0}{\rm I}} \over {{5^{3/2}}R}}$$

Answer

$${{4N{\mu _0}{\rm I}} \over {{5^{1/2}}R}}$$

Answer

$${{4N{\mu _0}{\rm I}} \over {{5^{3/2}}R}}$$

Magnetism and Matter

A Helmholtz coil has a pair of loops, each with $N turns and radius R. They are placed coaxially at distance R and the same current {\rm I} flows through the loops in the same direction. P, midway between the centers A and C$, is given by [Refer to figure given below] :

Choose the correct answer: