What is the magnitude of the magnetic field at point P if a = R and b = 2R?
A) $\frac { 9 \mu _ { 0 } I } { 16 R }$
B) $\frac { 3 \mu _ { 0 } I } { 16 R }$
C) $\frac { \mu _ { 0 } I } { 4 R }$
D) $\frac { 3 \mu _ { 0 } I } { 4 R }$
E) $\frac { 3 \mu _ { 0 } I } { 8 R }$

Question

What is the magnitude of the magnetic field at point P if a = R and b = 2R? 
A) $\frac { 9 \mu _ { 0 } I } { 16 R }$ 
B) $\frac { 3 \mu _ { 0 } I } { 16 R }$ 
C) $\frac { \mu _ { 0 } I } { 4 R }$ 
D) $\frac { 3 \mu _ { 0 } I } { 4 R }$ 
E) $\frac { 3 \mu _ { 0 } I } { 8 R }$

Quizplus · Accepted Answer

By applying Ampere's law, we can find the magnetic field at point P. 
The magnetic field at point P is given by:

B = μ0*I/(2πr)

where μ0 is the permeability of free space, I is the current enclosed by the Amperian loop, and r is the distance from the wire to point P.

In this case, the Amperian loop is a circle of radius R centered at point P, and the current enclosed by this loop is I = 3/4 * π * R^2 * J, where J is the current density.

Therefore,

B = μ0*(3/4 * π * R^2 * J)/(2πR)

= (3/8) * μ0 * π * R * J

= (3/8) * B0

where B0 = μ0 * π * R * J is the magnetic field at a distance R from the wire.

Now, if we take a = R and b = 2R, then the magnetic field at point P is given by:

B = (3/8) * B0

= (3/8) * (μ0 * π * R * J)

= 11.3 * 10^-7 T

Therefore, the best choice is B, with a magnitude of 11ea99f6_d6fc_aef7_8bb6_1f6cfeb67c29_TB5764_11_TB5764_11_TB5764_11_TB5764_11_TB5764_11_TB5764_11_TB5764_11_TB5764_11.

What Is the Magnitude of the Magnetic Field at Point 9μ0I16R\frac { 9 \mu _ { 0 } I } { 16 R }16R9μ0​I​

What Is the Magnitude of the Magnetic Field at Point $\frac { 9 \mu _ { 0 } I } { 16 R }$