We find that N current loops are coplanar and coaxial.The first has radius a and current I.The second has radius 2a and current 2I,and the pattern is repeated up to the Nth,which has radius Na and current NI.The current in each loop is counterclockwise as seen from above.The magnitude of the magnetic field at the center of the loops is
A) $\frac { \mu _ { 0 } I } { 2 N a }$ .
B) $\frac { \mu _ { 0 } I } { N a } .$
C) $\frac { \mu _ { 0 } I } { 2 a }$ .
D) $\frac { \mu _ { 0 } N I } { 2 a }$ .
E) $\frac { \mu _ { 0 } N I } { a }$ .

Question

Quizplus · Accepted Answer

The magnetic field at the center of a single loop is given by $ B = \frac{\mu_0 I}{2a} $. For N loops with increasing radius and current, the total magnetic field is the sum of the fields due to each loop, resulting in $ B = \frac{\mu_0 NI}{2a} $.

We Find That N Current Loops Are Coplanar and Coaxial μ0I2Na\frac { \mu _ { 0 } I } { 2 N a }2Naμ0​I​

We Find That N Current Loops Are Coplanar and Coaxial $\frac { \mu _ { 0 } I } { 2 N a }$