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There are two circular coils P and Q placed coaxially at a distance x from each other. Radius of P is a, and that of Q is b and a gt gt b. Current I is established in P for some time. Find the charge that flows through Q in this time interval. |
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Answer» Solution :Magnetic field due to the coil P at a distance x from its centre on its axis is given by the following relation: `B=(mu_(0)Ia^(2))/(2(a^(2)+x^(2))^(3 // 2))` Since coils are coaxial hence magnetic field is perpendicular to the plane of coil Q. Coil Q is very small, hence, we can assume field to be the same everywhere on the plane of coil Q Magnetic flux linked with the coil Q can be written as follows: `phi=B(PIB^(2))=(mu_(0)Ia^(2))/(2(a^(2)+x^(2))^(3 // 2))(pib^(2))` `phi=(mu_(0)piIa^(2)b^(2))/(2(a^(2)+x^(2))^(3 // 2))` Let current is turned off in time interval `Deltat` then final flux becomes zero and hence change in flux is same as initial flux. `DELTAPHI=(mu_(0)piIa^(2)b^(2))/(2(a^(2)+x^(2))^(3 // 2))` ...(i) Average emf induced in the coil Q. `EPSILON=(Deltaphi)/(Deltat)` Average current through the coil Q can be written as follows: `i=(epsilon)/(R)=(1)/(R)(Deltaphi)/(Deltat)` hence, charge flow through the coil Q can be written as follows: `Deltaq=iDeltat=(Deltaphi)/(R)` Substituting AP from equation (i) we get charge flow through the coil Q as follows: `Deltaq=(mu_(0)piIa^(2)b^(2))/(2R(a^(2)+x^(2))^(3 // 2))` |
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