Tutorial 8 — Magnetism (Subtopics 1-3)
Course: FAD1022 Basic Physics 2
Semester: 2 2025/2026
Prepared by: Dr Aisyah Hartini Jahidin
Given Constants
- Permeability of free space, $\mu_0 = 4\pi \times 10^{-7} \text{ T m A}^{-1}$
- Mass of electron, $m_e = 9.1 \times 10^{-31} \text{ kg}$
- Charge of electron, $e = 1.6 \times 10^{-19} \text{ C}$
Question 1
Two long, straight wires, wire 1 and wire 2, are positioned perpendicular to each other. The current in wire 2 is $I_2 = 1.2 \text{ A}$ (Figure 1).
Determine:
a) The direction and magnitude of the current $I_1$ if the resultant magnetic field at point $R$ is zero. b) If wire 1 carries current into the page and is placed 2 cm to the left of point R, oriented vertically relative to wire 2, determine the magnitude of the magnetic field at R using the value of $I_1$ from part (a).
Given distances:
- 5 cm from $I_1$ to R
- 3 cm from $I_2$ to R
Question 2
Three long straight wires Q, R and S, carry currents as shown in Figure 2.
Given:
- $I_Q = 3.0 \text{ A}$
- $I_R = 1.5 \text{ A}$
- $I_S = 3.0 \text{ A}$
- Distances forming right triangle with legs 3 cm and 4 cm
Determine the resultant of the magnetic field at point P.
Question 3
Two circular coils, each of radius 8 cm, are placed on the xy-plane (Figure 3).
Given:
- Coil 1: 5 turns, carries current $I_1 = 2 \text{ A}$ in the clockwise direction
- Coil 2: 10 turns, carries current $I_2$ in the counterclockwise direction
Calculate:
a) $I_2$ if the resultant magnetic field at the center of the coils is $-3.2 \times 10^{-5} \text{ T}$, in the -z-axis direction. b) Determine the direction of magnetic field outside the coils due to $I_1$.
Question 4
An electron moves undeflected in perpendicular electric and magnetic fields of $4.5 \times 10^4 \text{ V m}^{-1}$ and $3.8 \text{ mT}$, respectively. The electric field is then switched off, and the electron follows the path shown in Figure 4.
Calculate:
a) Derive an expression for the speed of the electron when it moves undeflected. b) Determine the direction of the magnetic field required for the electron to strike the wall. c) Calculate the radius of the circular motion. d. Determine the period of the motion.
Question 5
Three long, parallel wires carry currents as shown in Figure 5.
Given:
- $I_1 = 2 \text{ A}$
- $I_3 = 4 \text{ A}$
- Wire separation: 5.0 cm and 1.8 cm
Calculate:
a) The value of current $I_2$ if the resultant magnetic force per unit length on $I_1$ is zero. Provide your answer as an integer. b) If the resultant magnetic force per unit length acting on wire 1 is $6 \mu\text{N m}^{-1}$, calculate the value of current, $I_2$. c) Based on your answer in part (a), determine the resultant magnetic force per unit length acting on wire 1 if the direction of current in $I_2$ is reversed.
Additional Questions
Question A1
Two long wires Y and Z, each carrying a current of 10 A and are separated by 4 cm (Figure 1).
Calculate:
a) At each point P, Q, and R, calculate the resultant magnetic field produced by both wires Y and Z.
- Answers: $\sum B_P = -1.33 \times 10^{-4} \text{ T}$, $\sum B_Q = 0$, $\sum B_R = +1.33 \times 10^{-4} \text{ T}$
b) If the current in wire Z is directed into the page, determine the resultant magnetic field at point Q.
- Answer: $\sum B_Q = 2 \times 10^{-4} \text{ T}$
Question A2
An electron enters a uniform magnetic field of 2.5 T with a velocity of $1.5 \times 10^7 \text{ m/s}$ at an angle of $60°$ to the horizontal. The magnetic field is directed along the +y-axis.
Calculate:
a) The magnetic force acting on the proton — ans: $F = 3.0 \times 10^{-12} \text{ N}$ b) Determine the direction of the force immediately after the proton enters the magnetic field region — ans: Towards -z-axis
Related Concepts
- Magnetism
- Magnetic Field
- Biot-Savart Law
- Ampere's Law
- Magnetic Field of Straight Wire ($B = \frac{\mu_0 I}{2\pi r}$)
- Magnetic Field of Circular Coil ($B = \frac{\mu_0 NI}{2r}$)
- Lorentz Force
- Magnetic Force on Moving Charge ($\vec{F} = q\vec{v} \times \vec{B}$)
- Magnetic Force Between Wires
- Velocity Selector
- Circular Motion in Magnetic Field