Principles of Physics: A Calculus-Based Text
Principles of Physics: A Calculus-Based Text
5th Edition
ISBN: 9781133104261
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 22, Problem 42P

(a)

To determine

The possibility of the situation and any other possibility of the situation.

(a)

Expert Solution
Check Mark

Answer to Problem 42P

Yes, the situation is possible and the only possibility is placing the third wire at a distance at which the force between wire 1 and 3 balances the force between wire 2 and 3.

Explanation of Solution

Given info: The electric current in wire 1 is 1.50A in upward direction and the electric current in wire 2 is 4.00A in downward direction. The distance between wire 1 and wire 2 is 20.0cm

The orientation of the wires is shown in the figure below.

Principles of Physics: A Calculus-Based Text, Chapter 22, Problem 42P

Figure (1)

The formula to calculate the magnitude of force per unit length is,

F=LμI1I22πd (1)

Here,

I1 is the electric current in wire 1.

I2 is the electric current in wire 2.

d is the distance between the wires.

μ is the permeability of free space.

L is the length of wire on which force is calculated.

For the stability of wire 3 the magnetic force due to wire 1 on 3 must be equal to that of magnetic force due to wire 2 on 3

For equilibrium of wire 3,

F1on3=F2on3

From equation (1)

LμI1I32πd=LμI3I22π(x+d)

The above equation would be satisfied for only a particular position of wire 3 with respect to wire 1 and 2.

Thus, the situation is possible and the only possibility is placing the third wire at a distance at which the force between wire 1 and 3 balances the force between wire 2 and 3.

Conclusion:

Therefore, the situation is possible and the only possibility is placing the third wire at a distance at which the force between wire 1 and 3 balances the force between wire 2 and 3.

(b)

To determine

The position of wire 3.

(b)

Expert Solution
Check Mark

Answer to Problem 42P

The position of wire 3 is 12cm on the left of wire 1.

Explanation of Solution

Given info: The electric current in wire 1 is 1.50A in upward direction and the electric current in wire 2 is 4.00A in downward direction. The distance between wire 1 and wire 2 is 20.0cm

The formula to calculate the magnitude of force per unit length is,

F=LμI1I22πd (2)

Here,

I1 is the electric current in wire 1.

I2 is the electric current in wire 2.

d is the distance between the wires.

μ is the permeability of free space.

For the stability of wire 3 the magnetic force due to wire 1 on 3 must be equal to that of magnetic force due to wire 2 on 3

For equilibrium of wire 3,

F1on3=F2on3

From equation (2)

LμI1I32πd=LμI3I22π(x+d)I1d=I2(x+d)

Substitute 1.50A for I1 , 4.00A for I2 and 20.0cm for x in the above equation to find the value of d .

(1.50A)d=4.00A(20cm+d)4.0d=1.50(20cm+d)d=12cm

The distance of the wire 3 is 12cm on the left of wire 1.

Thus, the position of wire 3 is 12cm on the left of wire 1.

Conclusion:

Therefore, the position of wire 3 is 12cm on the left of wire 1.

(c)

To determine

The magnitude and direction of the current in wire 3.

(c)

Expert Solution
Check Mark

Answer to Problem 42P

The magnitude of current in wire 3 is 2.4A in downward direction.

Explanation of Solution

Given info: The electric current in wire 1 is 1.50A in upward direction and the electric current in wire 2 is 4.00A in downward direction. The distance between wire 1 and wire 2 is 20.0cm

For the stability of wire 1 the magnetic force due to wire 1 on 3 must be equal to that of magnetic force due to wire 2 on 1

For equilibrium of wire 3,

F3on1=F2on1

From equation (2)

LμI1I32πd=LμI1I22π(x+d)I3d1=I2d2

Here,

d1 is the distance between wire 1 and 3.

d2 is the distance between wire 1 and 2.

Substitute 4.00A for I2 , 12cm for d1 and 20.0cm for d2 in the above equation to find the value of I3 .

I3(12cm)=4.00A(20.0cm)I3=2.4A

The magnitude of electric current in wire 3 is 2.4A in downward direction as the current is in the same direction as that of the wire 2.

Conclusion:

Therefore, the magnitude of current in wire 3 is 2.4A in downward direction.

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Chapter 22 Solutions

Principles of Physics: A Calculus-Based Text

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