Question

An electron is moving in the north direction. It experiences a force in a vertically upward direction. The magnetic field at the position of the electron is in the direction of
A. East
B. West
C. North
D. South

Answer 1

Hint: When the charged particle moves in a region which contains magnetic field then there is force experienced by the charged particle which is proportional to the vector product of the velocity of the charged particle and the magnetic field vector.

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

Complete step by step solution:
It is given that the electron is moving towards the north direction. The electron is having a negative charge on it. The magnetic force on the electron is vertically upward. Taking the direction towards north as y-axis, south as –y-axis, east as +x-axis, west as –x-axis. The direction vertically upward will be +z-axis and the direction vertically downward is –z axis.

Using the magnetic force formula,
\[\overrightarrow F = q\left( {\overrightarrow v \times \overrightarrow B } \right)\]
\[\Rightarrow {F_0}\widehat k = - e\left( {{v_0}\widehat j \times \overrightarrow B } \right)\]
\[\Rightarrow - \left( {\dfrac{{{F_0}}}{{e{v_0}{B_0}}}} \right)\widehat k = \widehat j \times \widehat B\]
Using right handed triad system, \[\widehat j \times \widehat i = - \widehat k\]
So, the direction along the magnetic field is equivalent to\[\widehat i\], i.e. +x-axis.
As per the assumed direction equivalence, the +x-axis represents the direction along the East. So, the direction of the magnetic field is towards the East.

Therefore, the correct option is A.

Note: The direction of the magnetic field can also be determined using Fleming’s left hand rule. While using the vector method to determine the magnetic field we must be aware of the geographical direction equivalent to the Cartesian coordinate system.