Question

A proton experiences an eastward force of 30 × N while traveling in a magnetic field of 5 × T north. 

1. Find the magnitude of the proton’s velocity
2. State the direction of the proton’s velocity 
3. Draw the proton and indicate the directions of all three vectors using the appropriate notation as shown in the table above

Answer 1

To be given in question

Magnetic force(F)=30i

Magnetic field (B)=5j

To be asked in question

Part(a) magnitude of velocity

Part(b)=velocity direction

Part (c)=diagram

Part (a)

We know that

$F=q(v\times B)$

$F=qvBsin\theta\hat{n}$

$\hat{n} direction is (v\times B) direction$

Magnitude velocity

$v=\frac{F}{qB}$

Put value

$v=\frac{30}{1.6\times10^{-19}\times5}$

$v=3.75\times 10^{19}m/sec$

Part (b) state direction of proton velocity

$F=q(v\times B)$

$F=qvB\hat{n}$

$\hat{n} direction is$

$(v\times B)$ direction mean F direction (i) direction

$(v\times B)$ direction (i) direction possible then velocity direction (-k)

Then velocity direction

$v=v(-k)$

Nagetive z-axis direction of velocity direction

Part(c)

Vector form daigram

According to diagram velocity direction

$(-\hat{k})$