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A beam of ions passes undeflected through two parallel horizontal plates 1.5cm apart having a p.d of 3000v when a perpendicular magnetic field of 10-2T is applied and in the magnetic field alone beam is bent into a curve of radius 2m. Calculate the charge mass ratio of the ions
To calculate the charge-to-mass ratio of the ions, you will need to use the following formulas:
1. For the electric field:
F = q * E
where F is the force experienced by the ions, q is the charge of the ions, and E is the electric field strength.
2. For the magnetic field:
F = q * v * B
where F is the force experienced by the ions, q is the charge of the ions, v is their velocity, and B is the magnetic field strength.
3. For the centripetal force:
F = (m * v^2) / r
where F is the force experienced by the ions, m is the mass of the ions, v is their velocity, and r is the radius of the curve.
Now let's solve step by step:
1. Electric field force:
Since the ions pass undeflected through the plates, the electric force is balanced by the magnetic force acting on the ions. Therefore:
q * E = q * v * B
Since both plates have a potential difference (p.d) of 3000V and are 1.5cm (0.015m) apart, we can find the electric field strength using:
E = V / d
where V is the p.d and d is the distance between the plates.
E = 3000V / 0.015m
2. Magnetic field force:
We are given that the magnetic field strength is 10^(-2)T. The ions are bent into a curve of radius 2m. Hence:
q * v * B = (m * v^2) / r
We can rearrange this equation to solve for the charge-to-mass ratio (q/m):
q/m = (v * B * r) / v^2
q/m = (B * r) / v
Now we need to find the velocity of the ions.
3. Finding velocity:
Since the ions pass undeflected through the plates, the electric force is balanced by the magnetic force. Therefore:
q * E = q * v * B
Divide both sides by q:
E = v * B
Solve for v:
v = E / B
Substitute the value of E and B we found earlier and calculate v.
4. Calculating q/m:
Substitute the values of B, r, and v into the equation:
q/m = (B * r) / v
Calculate the value of q/m using the given values.
By following these steps, you can calculate the charge-to-mass ratio of the ions.