Shortcuts and Tricks for Solving Numerical Problems

Integers

• Solenoids: Use the formula $$B={\mu }_{0}nI/l$$, where B is the magnetic field strength, $${\mu }_0$$ is the permeability of free space $$(4\times {10}^{-7}\text{ T}\cdot \text{m/A})$$, n is the number of turns in the solenoid, I is the current flowing through the solenoid, and l is the length of the solenoid.

• Toroids: Use the formula $$B={\mu }_{0}nI/(2\pi r)$$, where B is the magnetic field strength, $${\mu }_0$$ is the permeability of free space, n is the number of turns in the toroid, I is the current flowing through the toroid, and r is the radius of the toroid.

• Magnetic force between two long straight wires: Use the formula $$F=\frac{{\mu }_0{I}_1{I}_2}{2\pi d}$$, where F is the magnetic force between the wires, $${\mu }_0$$ is the permeability of free space, I1 is the current flowing through the first wire, I2 is the current flowing through the second wire, and d is the distance between the wires.

Fractions

• Magnetic field strength inside a long straight wire: Use the formula $$B=\frac{{\mu }_{0}I}{2\pi d}$$, where B is the magnetic field strength, $${\mu }_0$$ is the permeability of free space, I is the current flowing through the wire, and d is the distance from the wire.

Decimals

• Magnetic field strength of a circular loop: Use the formula $$B=\frac{{\mu }_{0}I}{4\pi r}[\sin ({\theta }_1)+\sin ({\theta }_2)]$$, where B is the magnetic field strength, $${\mu }_0$$ is the permeability of free space, I is the current flowing through the loop, r is the radius of the loop, and $${\theta }_1\text{and}{\theta }_2$$ are the angles between the line from the center of the loop to the observation point and the normal to the loop at that point.

Powers

• Magnetic moment of a current loop: Use the formula $$\mu =IA$$, where $$\mu$$ is the magnetic moment, I is the current flowing through the loop, A is the area of the loop.

Algebraic expressions

• Magnetic field strength of a solenoid: Use the formula $$B=nI{\mu }_0$$, where B is the magnetic field strength inside the solenoid, n is the number of turns in the solenoid per unit length, I is the current flowing through the solenoid, and $${\mu }_0$$ is the permeability of free space.

Equations

• Ampere’s law: (\sum Bdl=\mu_0I), where $${\mu }_0$$ is the permeability of free space, I is the current passing through the loop, and the summation (\sum\space Bdl) is around a closed loop.

• Magnetic field strength of a toroid: Use the formula $$B=nI\frac{{\mu }_0}{2\pi r}$$, where B is the magnetic field strength inside the toroid, n is the number of turns in the toroid, I is the current flowing through the toroid, r is the radius of the toroid, and $${\mu }_0$$ is the permeability of free space.

Graphs

• Magnetic field strength vs. distance from a long straight wire: The graph shows that the magnetic field strength decreases with increasing distance from the wire.

• Magnetic field strength vs. angle from a circular loop: The graph shows that the magnetic field strength is maximum at the center of the loop and decreases with increasing angle from the center.

Tables

• Comparison of different types of magnetic fields: The table compares the different types of magnetic fields, their equations, and their applications.