1) What is B y (P), the y-component of the magnetic field at point P, located a
ID: 1785539 • Letter: 1
Question
1)
What is By(P), the y-component of the magnetic field at point P, located a distance d = 31 cm from the origin along the x-axis as shown?
T
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Computed value:
0
Submitted:
Monday, October 23 at 9:57 PM
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The magnetic field at point P is not zero. The wire and the cylindrical shell both produce magnetic fields at point P. The total magnetic field at point P is equal to the vector sum of the fields created by the wire and by the cylindrical shell separately.
2)
What is
PSBdlPSBdl
where the integral is taken along the dotted path shown in the figure above: first from point P to point R at (x,y) = (0.707d, 0.707d), and then to point S at (x,y) = (0.6d, 0.6d).
T-m
Your submissions:
0
Computed value:
0
Submitted:
Monday, October 23 at 10:01 PM
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The integral of B dot dl from P to S is not zero. You may be thinking of using Ampere law here, but remember that the integral in Ampere law is over a closed path. This integral is from P to S. It is not a closed path. Therefore, there is no meaning to enclosed current. To answer this questin, you do need ot do the integral.
3)
What is By(T), the y-component of the magnetic field at point T, located at (x,y) = (-5 cm,0), as shown?
T
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4)
What is
SPBdlSPBdl
where the integral is taken on the straight line path from point S to point P as shown?
T-m
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5)
Suppose the magnitude of the current I2 is now doubled. How does the magnitude of the magnetic field at (x,y) = (2.15 cm, 0) change?
B(2.15 cm, 0) increases
B(2.15 cm, 0) decreases
B(2.15 cm, 0) remains the same
Explanation / Answer
a)
Due to symmetry we can draw loop at 31 cm
B(2pi*d) = u0*(I1+I2)
B = u0*(I1+I2) / 2pi*d
=> B = (4pi*10^-7*(-2.1+7.4))/(2pi*0.31)
=> B = 3.42*10^-6 T
b)
Section RS gives 0 since B.dl gives 0
Section PR is 1/8 of complete loop,
So,
B = 1/8 Bdl
= 1/8*u0*I
= 1/8*(4pi*10^-7)*(-2.1+7.4)
= 8.32*10^-7 T
c)
I2_encl = I2(pi(r^2-a^2)/(pi*(b^2-a^2)
= (7.4)(5^2-4.3^2)/(6.2^2-4.3^2)
= 2.415 A
BT = -u0*(I1+I2_encl)/2pi*r
= - 4pi*10^-7*(-2.1+2.415)/(2pi*0.05)
= 1.3*10^-6 T
d)
- 8.32*10^-7 T
e)
Points inside radius are not affected by I2, so remain the same.
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