Question

A uniform electric field and a uniform magnetic field exist in a region in the same direction. An electron is projected with velocity pointed in the same direction the electron will:
A) Turn to its right
B) Turn to its left
C) Keep moving in the same direction but its speed will increase
D) Keep moving in the same direction but its speed will decrease

Answer 1

Hint: Recall that the electric field is the region around a charged particle or any object having charge within which its influence can be felt. In other words, this charged particle will have an effect on the objects in the surrounding area. Similarly a magnetic field is the space around a magnet where its influence can be felt.

Complete solution:
Step I: Force due to magnetic field is given by using the formula$ = q(\overrightarrow V \times \overrightarrow B )$
Since velocity and field are in the same direction, so the angle between them is zero.
The cross product of two vectors can be written as$ = qVB\sin 0$
$\therefore $force due to the magnetic field will also be equal to zero.
$ \Rightarrow {F_B} = 0$

Step II: Force due to electric field is given by the formula ${F_E} = qE$.
Since electrons have a negative charge, the direction of force will be opposite to that of the direction of the electric field. The force will be then written as
$ \Rightarrow {F_E} = - qE$
Since the force due to the magnetic field is zero, the electron will be moving only under the influence of the electric field. So, the electron will be moving in the same direction but its speed will decrease.

Option D is the correct answer.

Note: It is important to remember the electric field and the magnetic field and the electric field exist simultaneously. This means a changing electric field creates a magnetic field and a changing magnetic field creates an electric field. Electricity and magnetism are phenomena related to each other and are related in a field called electromagnetic field.