
Concept explainers
(a)
The magnetic force on each side of the loop.
(a)

Answer to Problem 52P
The magnetic force on each side of the loop is given in table 1.
Explanation of Solution
Refer figure 1.
Write an expression for the force on the side.
F=ILBsinθ (I)
Here,F is the magnitude of the force, I is the magnitude of the current, L is the length of the wire, B is the magnitude of magnetic field and θ is the angle.
Conclusion:
Consider the top side of the loop:
Substitute 1.0 A for I, 30.0 cm for L, 2.5 T for B and 60.0° for θ in equation (I) to find F.
F=(1.0 A)((30.0 cm)(1 m102 cm))(2.5 T)sin(60.0°)=(1.0 A)(0.300 m)(2.5 T)sin(60.0°)=0.65 N
Consider the right side of the loop:
Substitute 1.0 A for I, 20.0 cm for L, 2.5 T for B and 30.0° for θ in equation (I) to find F.
F=(1.0 A)((20.0 cm)(1 m102 cm))(2.5 T)sin(30.0°)=(1.0 A)(0.200 m)(2.5 T)sin(30.0°)=0.25 N
Consider the bottom side of the loop:
Substitute 1.0 A for I, 30.0 cm for L, 2.5 T for B and 120° for θ in equation (I) to find F.
F=(1.0 A)((30.0 cm)(1 m102 cm))(2.5 T)sin(120°)=(1.0 A)(0.300 m)(2.5 T)sin(120°)=0.65 N
Consider the left side of the loop:
Substitute 1.0 A for I, 20.0 cm for L, 2.5 T for B and 150° for θ in equation (I) to find F.
F=(1.0 A)((20.0 cm)(1 m102 cm))(2.5 T)sin(150°)=(1.0 A)(0.200 m)(2.5 T)sin(150°)=0.25 N
According to right hand rule, if the thumb, index finger and middle finger are kept perpendicular to each other, the thumb points towards the direction of force if the index finger is kept along the magnetic field and the middle finger is kept along the direction of current.
Thus, the magnetic force on each side of the loop is given in table 1.
Side | →L | θ | F(N) | Direction of →F |
Top | 0.300 m right | 60.0° | 0.65 | Into the page |
Right | 0.200 m down | 30.0° | 0.25 | Out of the page |
Bottom | 0.300 m right | 120° | 0.65 | Out of the page |
Left | 0.200 m up | 150° | 0.25 | Into the page |
Table 1
(b)
The net magnetic force on the loop.
(b)

Answer to Problem 52P
The net magnetic force on the loop is 0.
Explanation of Solution
Write an expression for the net magnetic force.
Σ→F=→Ftop+→Fbottom+→Fright+→Fleft (II)
Σ→F is the net magnetic force, →Ftop is the magnetic force on top side, →Fbottom is the magnetic force on bottom side, →Fleft is the magnetic force on left side and →Fright is the magnetic force on right side.
Conclusion:
Substitute 0.65 N in for →Ftop, 0.65 N out for →Fbottom, 0.25 N in for →Fleft and 0.25 N out for →Fright
Σ→F=0.65 N in+0.65 N out+0.25 N in+0.25 N out=0
Thus, the net magnetic force on the loop is 0.
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Chapter 19 Solutions
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