Worksheet: Electromagnetic Interactions between Straight Conductors

In this worksheet, we will practice determining the magnetic forces between parallel lines of current and analyzing the net magnetic fields of the currents.

Q1:

Two long, straight, parallel conducting wires are separated by distance 𝑑 = 1 5 c m , as shown in the diagram. The wires both carry 1.2 A currents in the same direction. What is the magnitude of the force that a length 𝐿 = 2 . 5 m of each wire exerts on the other? Use a value of 4 𝜋 × 1 0 H/m for the magnetic permeability of the region between the wires.

  • A 2 4 × 1 0 N
  • B 4 . 8 × 1 0 N
  • C 9 . 6 × 1 0 N
  • D 2 . 4 × 1 0 N
  • E 4 8 × 1 0 N

Q2:

The diagram shows the field lines of the magnetic field of two parallel current-carrying conductors. The right-hand current goes into the plane of the diagram and the left-hand current goes out of the plane of the diagram. The currents have the same magnitude.

What is the direction of the net magnetic field at point 𝐴 ?

  • AThere is no net magnetic field.
  • BNegative 𝑦 -direction
  • CPositive 𝑦 -direction
  • DNegative 𝑥 -direction
  • EPositive 𝑥 -direction

What is the direction of the net magnetic field at point 𝐵 ?

  • AThere is no net magnetic field.
  • BNegative 𝑥 -direction
  • CPositive 𝑦 -direction
  • DPositive 𝑥 -direction
  • ENegative 𝑦 -direction

What is the direction of the net magnetic field at point 𝐶 ?

  • APositive 𝑥 -direction
  • BThere is no net magnetic field.
  • CNegative 𝑦 -direction
  • DPositive 𝑦 -direction
  • ENegative 𝑥 -direction

What is the direction of the net magnetic field at point 𝐷 ?

  • APositive 𝑦 -direction
  • BNegative 𝑦 -direction
  • CPositive 𝑥 -direction
  • DNegative 𝑥 -direction
  • EThere is no net magnetic field.

What is the direction of the net magnetic field at point 𝐸 ?

  • AThere is no net magnetic field.
  • BNegative 𝑥 -direction
  • CPositive 𝑦 -direction
  • DNegative 𝑦 -direction
  • EPositive 𝑥 -direction

Q3:

The diagram shows the field lines of the magnetic field of two parallel current-carrying conductors. Both currents go into the plane of the diagram and they have the same magnitude.

What is the direction of the net magnetic field at point 𝐴 ?

  • ANegative 𝑥 -direction
  • BThere is no net magnetic field.
  • CPositive 𝑥 -direction
  • DPositive 𝑦 -direction
  • ENegative 𝑦 -direction

What is the direction of the net magnetic field at point 𝐵 ?

  • AThere is no net magnetic field.
  • BNegative 𝑦 -direction
  • CPositive 𝑦 -direction
  • DPositive 𝑥 -direction
  • ENegative 𝑥 -direction

What is the direction of the net magnetic field at point 𝐶 ?

  • APositive 𝑥 -direction
  • BNegative 𝑦 -direction
  • CNegative 𝑥 -direction
  • DPositive 𝑦 -direction
  • EThere is no net magnetic field.

What is the direction of the net magnetic field at point 𝐷 ?

  • APositive 𝑥 -direction
  • BPositive 𝑦 -direction
  • CNegative 𝑥 -direction
  • DThere is no net magnetic field.
  • ENegative 𝑦 -direction

What is the direction of the net magnetic field at point 𝐸 ?

  • ANegative 𝑥 -direction
  • BPositive 𝑦 -direction
  • CThere is no net magnetic field.
  • DPositive 𝑥 -direction
  • ENegative 𝑦 -direction

Q4:

Several horizontal pairs of parallel conducting wires are stacked vertically. The magnitude of the current in each wire is the same.

Which of the configurations of current directions shown is equivalent to that of a cross section of a solenoid?

  • A
  • B
  • C

Would the direction of the magnetic field along the axis of the solenoid be upward or downward?

  • ADownward
  • BUpward

Q5:

The diagram shows concentric field lines of the magnetic fields of two parallel current-carrying conductors. Both currents are into the plane of the diagram, and the currents have the same magnitude as each other. The increase in radius of the concentric field lines is constant, and the strength of a magnetic field at a point around a current is proportional to the perpendicular distance of the point from the current.

Which of the following lists of the points shown in the diagram correctly orders the points from greatest to smallest magnitude of net magnetic field?

  • A 𝐴 , 𝐵 , 𝐶 , 𝐷 , 𝐸
  • B 𝐷 , 𝐴 , 𝐸 , 𝐶 , 𝐵
  • C 𝐸 , 𝐵 , 𝐶 , 𝐴 , 𝐷
  • D 𝐵 , 𝐶 , 𝐸 , 𝐴 , 𝐷
  • E 𝐵 , 𝐸 , 𝐶 , 𝐴 , 𝐷

Q6:

The diagram shows concentric field lines of the magnetic fields of two parallel current-carrying conductors. The right-hand current goes into the plane of the diagram and the left-hand current goes out of the plane of the diagram. The currents have the same magnitude as each other. The increase in the radius of the concentric field lines is constant, and the strength of a magnetic field at a point around a current is inversely proportional to the perpendicular distance of the point from the current.

Which of the following lists of the points shown in the diagram correctly orders the points from the greatest to the smallest magnitude of net magnetic field?

  • A 𝐴 , 𝐵 , 𝐸 , 𝐶 , 𝐷
  • B 𝐸 , 𝐵 , 𝐴 , 𝐶 , 𝐷
  • C 𝐷 , 𝐸 , 𝐶 , 𝐵 , 𝐴
  • D 𝐷 , 𝐶 , 𝐸 , 𝐵 , 𝐴
  • E 𝐴 , 𝐸 , 𝐶 , 𝐵 , 𝐷

Q7:

Three long, straight, parallel, conducting wires 𝑊 , 𝑊 , and 𝑊 carry currents of 1.6 A, 1.1 A, and 1 . 9 A respectively. 𝑊 is 2.5 cm from 𝑊 and 5.1 cm from 𝑊 . 𝑊 is located between the other two wires. Find the magnitude of the force per meter of length on 𝑊 perpendicular to 𝑊 . Use a value of 4 𝜋 × 1 0 H/m for the magnetic permeability of the region between the wires.

  • A 3 6 × 1 0 N/m
  • B 4 5 × 1 0 N/m
  • C 2 . 2 × 1 0 N/m
  • D 4 . 4 × 1 0 N/m
  • E 1 . 1 × 1 0 N/m

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