Questions 54-55
What is the magnitude of the net force on the loop when the induced current is i?
A. "\frac{\mu_0 i I}{2\pi} \ln \left ( \frac{r+a}{r} \right)")
B. "\frac{\mu_0 i I}{2\pi} \ln \left ( \frac{r}{r+a} \right )")
C.
D.} "\frac{\mu_0 i I}{2\pi} \frac{ab}{r(r+a)}")
E.}{ab} "\frac{\mu_0 i I}{2\pi} \frac{r(r+a)}{ab}")
Solution:
Magnetic force on an electric current: "\vec{F} = l(\vec{I}\times \vec{B})")
For the loop, induced current I = i is parallel to B, and l = b
→ F = ibB
Ampere's Law for a magnetic field around a straight wire:
→
Only choice D fits the above equation.
Answer: D
Complete calculation:
On the left, r → r
On the right, r → r + a
 "= \frac{\mu_0 iIb}{ 2\pi} \left ( -\frac{1}{r}+\frac{1}{r+a} \right )")
} "=-\frac{\mu_0 iI}{ 2\pi} \frac{ab}{r(r+a)}")
Note: since force on the left is directed to the left → negative sign
The magnitude is} "|F_{\text{total}}|=\frac{\mu_0 i I}{2\pi} \frac{ab}{r(r+a)}")
A rectangular loop of wire with dimensions shown above is coplanar with a long wire carrying current I. The distance between the wire and the left side of the loop is r. The loop is pulled to the right as indicated.
What is the magnitude of the net force on the loop when the induced current is i?
A.
B.
C.
D.
E.
(GR9277 #55)
Solution:
Magnetic force on an electric current:
For the loop, induced current I = i is parallel to B, and l = b
→ F = ibB
Ampere's Law for a magnetic field around a straight wire:
→
Only choice D fits the above equation.
Answer: D
Complete calculation:
On the left, r → r
On the right, r → r + a
Note: since force on the left is directed to the left → negative sign
The magnitude is
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