Question

If an electron enters a magnetic field with its velocity pointing in the same direction as the magnetic field, then
A. The electron will turn to its right
B. The electron will turn to its left
C. The velocity of the electron will increase
D. The velocity of the electron will remain unchanged

Answer 1

Hint:Using the Fleming’s left hand rule or the Lorentz’s force law we can determine the force acting on the charged particle moving in a region of the uniform magnetic field. When we use Lorentz's force law we make equivalence of the geographic direction with the Cartesian coordinate system.

Formula used:
\[\overrightarrow F = q\left( {\overrightarrow v \times \overrightarrow B } \right)\]
Here is the force acting on the charged particle moving with velocity in a region of magnetic field

Complete step by step solution:
Let the electron is travelling in +x-axis direction with speed v. Then the velocity vector will be \[\overrightarrow v = v\widehat i\]. It is given that the velocity is in the same direction as the magnetic field vector. So the magnetic field is also in the direction along +x-axis.

If the magnetic field strength is B then the magnetic field vector is,
\[\overrightarrow B = B\widehat i\]
Then the magnetic force on the electron is,
\[\overrightarrow F = - e\left( {v\widehat i \times B\widehat i} \right)\]
\[\Rightarrow \overrightarrow F = - evB \times 0\]
\[\therefore \overrightarrow F = 0\]
So, the magnetic force acting on the electron is zero; so there will be no deflection in the electron. Hence, The velocity of the electron will remain unchanged.

Therefore, the correct option is D.

Note: The angle between two vectors which are directed in the same direction is zero. The sine of the angle which is zero is zero. So, the magnitude of the magnetic force is zero. The deflection is in the direction of the force, as force is zero so there will be no deflection.