Question

Consider a toroid of circular cross-section of radius b, major radius R much greater than minor radius b. Find the total energy stored in toroid. (I is current)

• A. $\frac { \mu _ { 0 } \mathrm {~N} ^ { 2 } \mathrm { I } ^ { 2 } \mathrm {~b} ^ { 2 } } { 2 \mathrm { R } }$
• B.
• C.
• D. $\frac { \mu _ { 0 } \mathrm {~N} ^ { 2 } \mathrm { I } ^ { 2 } \mathrm {~b} ^ { 2 } } { 4 \mathrm { R } }$

Answer 1

Answer: (A)

$\frac { \mu _ { 0 } \mathrm {~N} ^ { 2 } \mathrm { I } ^ { 2 } \mathrm {~b} ^ { 2 } } { 2 \mathrm { R } }$

Answer 2

The point charge moves in circle as shown in figure. The magnetic field vectors at a point P on axis of circle are $\overrightarrow { \mathrm { B } } _ { \mathrm { A } }$ and at the instants the point charge is at A and C respectively as shown in the figure.

Hence as the particles rotates in circle, only magnitude of magnetic fiels remains constant at the point on axis P but it's direction changes. Ž Alternate solution Ž The magnetic field at point on the axis due to charged particle moving along a circular path is given by

$\frac { \mu _ { 0 } } { 4 \pi }$ $\frac { \mathrm { q } \overrightarrow { \mathrm { v } } \times \overrightarrow { \mathrm { r } } } { \mathrm { r } ^ { 3 } }$ It can be seen that the magnitude of the magnetic field at on point on the axis remains constant. But the direction of the field keeps on changing.