Question

When an electron enters
uniform magnetic field at an acute
angle, its path will be
Answer
A.O straight line
B. Circular
C.O Helical
Any of the above​

Answer 1

Answer:

Explanation:

The force (F) on wire of length L carrying a current I in a magnetic field of strength B is given by the equation:

F = BIL

But Q = It and since Q = e for an electron and v = L/t you can show that :

Magnetic force on an electron = BIL = B[e/t][vt] = Bev where v is the electron velocity

In a magnetic field the force is always at right angles to the motion of the electron (Fleming's left hand rule) and so the resulting path of the electron is circular (Figure 1).

Therefore :

Magnetic force = Bev = mv2/r = centripetal force

v = [Ber]/m

and so you can see from these equations that as the electron slows down the radius of its orbit decreases.

Charged particles move in circles at a constant speed if projected into a magnetic field at right angles to the field.

Charged particles move in straight lines at a constant speed if projected into a magnetic field along the direction of the field.

Figure 2 shows a 3D diagram of and electron moving at right angles to a uniform magnetic field.

If the electron enters the field at an angle to the field direction the resulting path of the electron (or indeed any charged particle) will be helical as shown in figure 3. Such motion occurs above the poles of the Earth where charges particles from the Sun spiral through the Earth's field to produce the aurorae.

 

Path of an electron in an electric field

We will consider next the case of an electron entering a uniform electroc field between two parallel plates (Figure 4). The potential difference between the plates is V and the plates are aligned along the x direction and the electron enters the field at right angles to the field lines:

The force on the electron is given by the equation:

F = eE = eV/d = ma

But since there is a force the electron must accelerate in the y direction and the acceleration is given by a = 2y/t2. (From the equation s = y = ut + ½ at2)

Therefore if we combine these to equations F = m2s/t2 and at right angles to then field x = vt so the equation for the path of the electron is:

eV/d = m2y/t2 = 2myv2/x2 or: