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Question

An electron is traveling horizontally towards the east. A magnetic field in a vertically downward direction exerts a force on the electron along____


  1. East

  2. West

  3. North

  4. South

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Solution

The correct option is C

North


Step 1: Define the forces

Given, the electron is moving horizontally towards east and magnetic field is vertically downward.
East is along the positive x-axis and vertically downward is along the negative z-axis.
From the conventions of vector notation, i^is the unit vector along the positive x-axis, and -k^ is the unit vector along the negative z-axis.

Then the velocity vector of the electron can be given as,
v=ai^+0j^+0k^

where a is the magnitude of the velocity.

Similarly, the magnetic field vector can be given as,
B=0i^+0j^-bk^

where b is the magnitude of the magnetic field.

Step 2: Formulas used

We know that when a charged particle is moving in a magnetic field it experiences a force on it which is given as,
F=qv×B

where q is the charge of the particle, v is the velocity vector of the particle and B is the magnetic field vector.

If a and b are vectors such that a=a1i^+a2j^+a3k^ and b=b1i^+b2j^+b3k^ then their cross-product is,
a×b=a2b3-b2a3i^+a3b1-b3a1j^+a1b2-b1a2k^

Step 3: Substitute values in the formula

Substituting the values of the terms in the force equation,

F=qv×B
F=qai^+0j^+0k^×0i^+0j^-bk^=q0-b-0·0i^+0·0--baj^+a·0-0·0k^F=q·abj^

Therefore the vector of the force on the electron is F=q·abj^.

Step 4: Interpret the direction of the force

The vector part of the force is abj^ and the unit vector along the direction of force is j^.
From the conventions of vector notation, we see that j^ is along the North.

Therefore the direction of force is along the North.

Hence, option C is correct.


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