# Multiple choice question about electric fields and magnetic fields

• MHB
• AztecChaze
In summary, the electron's speed can be calculated using the Lorentz law and the given values of the electric and magnetic fields. Plugging in the values, the speed is determined to be 1.32 km/s.
AztecChaze
Consider a region where a 25-volt-per-meter electric field and a 15-millitesla magnetic field exist and are along the same direction. If the electron is in the said region, is moving at a direction 20 degrees counter-clockwise from the direction of the magnetic field, and is experiencing a total force of 5 × 10-18 Newtons, determine the speed of the electron. Assume the velocity vector, the electric field, and the magnetic field are all lying on the same plane.

a.) 10.46 km/s
b.) 1.32 km/s
c.) 3.65 km/s
d.) 5.20 km/s

By the Lorentz law, the electromagnetic force is given by $\mathbf{F} = -e(\mathbf{E} + \mathbf{v} \times \mathbf{B})$, where $e$ is the elementary charge, equal to $1.6 \times 10^{-19} C$. Since the electric and magnetic fields point in the same direction, we may suppose that they are in the $x$-direction. Then $\mathbf{v} \times \mathbf{B}$ points in the negative z-direction and has magnitude $vB\sin(20^\circ)$. Therefore $\mathbf{F} = -e(E\,\mathbf{\hat{x}} - vB\sin(20^\circ)\,\mathbf{\hat{z}})$. Taking the square of the magnitude on both sides of the vector equation yields $F^2 = e^2[E^2 + (vB \sin 20^\circ)^2]$. Solving for $v$ results in $$v = \frac1{B\sin20^\circ}\sqrt{\left(\frac{F}{e}\right)^2 - E^2}$$ Plug in the given values of $F$, $E$ and $B$ into this formula to determine the answer.

## 1. What is the difference between electric fields and magnetic fields?

Electric fields are created by stationary electric charges, while magnetic fields are created by moving electric charges. Electric fields exert a force on other charges, while magnetic fields exert a force on moving charges.

## 2. How are electric fields and magnetic fields related?

Electric fields and magnetic fields are closely related, as they are both components of the electromagnetic force. They are also perpendicular to each other in most cases.

## 3. Can electric fields and magnetic fields exist independently of each other?

No, electric fields and magnetic fields are always interconnected and cannot exist without each other. This is known as the electromagnetic force.

## 4. How do electric fields and magnetic fields affect each other?

Electric fields and magnetic fields can interact with each other, causing a phenomenon known as electromagnetic induction. This is when a changing magnetic field creates an electric field, or vice versa.

## 5. What are some real-life applications of electric and magnetic fields?

Electric and magnetic fields have many practical applications, such as in generators, motors, and transformers. They are also used in technologies such as MRI machines, particle accelerators, and televisions.

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