Question

A charge + Q is moving upwards vertically. It enters a magnetic field directed to the north. The force on the charge will be towards
A. North
B. South
C. East
D. West

Answer 1

Hint: When a charged particle moves in a magnetic field then it experiences magnetic force which acts perpendicular to the direction of the motion of the charged particle and the magnetic field present in the field.



Formula used:
\[\overrightarrow F = q\left( {\overrightarrow v \times \overrightarrow B } \right)\], F is the magnetic force acting on the charge q with velocity v and magnetic field B.


Complete answer:
It is given the given charge is positive charge with magnitude Q,
\[q = + Q\]
Let the direction towards north is equivalent to the y-axis of the Cartesian coordinate system, then the south will be represented by –y-axis, east by +x-axis and west by –x-axis; the direction vertically upward will be +z-axis and the direction vertically downward is –z-axis.
So, the velocity and magnetic field vector of the charged particle can be written as,
The motion of the given charged particle is given vertically upwards. Let the speed of the charged particle is \[{v_0}\]
\[\overrightarrow v = {v_0}\widehat k\]
The magnetic field is towards the north, let the magnitude of the magnetic field strength is \[{B_0}\]
\[\overrightarrow B = {B_0}\widehat j\]
Using the magnetic force formula,
\[\overrightarrow F = + Q\left( {{v_0}\widehat k \times {B_0}\widehat j} \right)\]
\[\overrightarrow F = + Q{v_0}{B_0}\left( {\widehat k \times \widehat j} \right)\]
\[\overrightarrow F = + Q{v_0}{B_0}\left( { - \widehat i} \right)\]
\[\overrightarrow F = - Q{v_0}{B_0}\widehat i\]
So, the direction of the magnetic force on the charged particle is towards the negative x-axis, i.e. towards west.
Therefore, the correct option is (D).




Note:The direction of the magnetic force on the charged particle moving in a magnetic field can also be determined using Fleming’s right hand rule. While using the vector product method, we should be careful about the directions equivalent to the Cartesian coordinate system.