Question

Consider a toroid of circular cross-section of radius b, major radius R much greater than minor radius b, (see diagram) find the total energy stored in magnetic field of toroid–

• A.
• B.
• C. $\frac { B ^ { 2 } \pi ^ { 2 } b ^ { 2 } R } { 8 \mu _ { 0 } }$
• D. $\frac { B ^ { 2 } \pi ^ { 2 } b ^ { 2 } R } { \mu _ { 0 } }$

Answer 1

Answer: (D)

$\frac { B ^ { 2 } \pi ^ { 2 } b ^ { 2 } R } { \mu _ { 0 } }$

Answer 2

B = $\frac { \mu _ { 0 } \mathrm { Ni } } { 2 \mathrm { R } }$ f = pb² × B × N

f = Li L = $\frac { \phi } { \mathrm { i } }$ = $\frac { \mu _ { 0 } \mathrm {~N} ^ { 2 } \mathrm {~b} ^ { 2 } } { 2 \mathrm { R } }$ , with b <<< R

Energy = $\frac { 1 } { 2 }$Li² = $\frac { \mu _ { 0 } \mathrm {~N} ^ { 2 } \mathrm { i } ^ { 2 } } { 4 \mathrm { R } }$ b²