Consider a cubic region 28.5 cm on a side, in which a very good vacuum is mainta

Question

Consider a cubic region 28.5 cm on a side, in which a very good vacuum is maintained. It's top and bottom consist of conducting plates held at a potential difference of 7.50X10^5 V. Its left and right sides are the poles of a magnet with a field strength of .312 T, that can be considered uniform. It's front and back are sheets of glass, through which the experimenter can see what's happening. A particle with a mass of 8.05X10^-7 kg and a positive charge of 7.78X10^-8 C is released from rest at center of the plate at the high potential.
*If the electric field alone were acting in the charges particle, how much force would it exert & Still considering only the electric field how fast would the particle be going immediately before hitting the grounded plate & Find the magnitude of the magnetic force on the particle when it reaches its highest speed & by how much would you expect it to curve. Consider a cubic region 28.5 cm on a side, in which a very good vacuum is maintained. It's top and bottom consist of conducting plates held at a potential difference of 7.50X10^5 V. Its left and right sides are the poles of a magnet with a field strength of .312 T, that can be considered uniform. It's front and back are sheets of glass, through which the experimenter can see what's happening. A particle with a mass of 8.05X10^-7 kg and a positive charge of 7.78X10^-8 C is released from rest at center of the plate at the high potential.
*If the electric field alone were acting in the charges particle, how much force would it exert & Still considering only the electric field how fast would the particle be going immediately before hitting the grounded plate & Find the magnitude of the magnetic force on the particle when it reaches its highest speed & by how much would you expect it to curve.
*If the electric field alone were acting in the charges particle, how much force would it exert & Still considering only the electric field how fast would the particle be going immediately before hitting the grounded plate & Find the magnitude of the magnetic force on the particle when it reaches its highest speed & by how much would you expect it to curve.

Explanation / Answer

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let this be the position of two conducting plates, P denotes the ,initial position of our particle (which is rest at center of the plate at the high potential).

1) when Electric field alone acts on particle,

force on particle , Fe = q E

(Fe= force due to electric field on particle, q = charge of particle , E = Electric field strength)

and V = E d

(V = potential difference between conducting plates, d = distance between the plates, E same as above)

using values of V and d

7.50X105 = E x (28.5x 10-2m)

solving E = 2.63 x 106 N/C

hence Electric force Fe = q E = 7.78X10-8 C x 2.63 x 106 N/C = 0.205 N

Let m denote the mass of particle,

v1 = particles initial velocity, v2 = particles final velocity before hitting the plate

in question v1 = 0 (particle at rest initially)

Now to determine velocity before hitting the plate, we use the conservation of energy

i.e Initial potential energy = Final kinetic energy

q V = (0.5mv22 - 0.5 m v12)

7.78X10-8 x 7.50X105 = [0.5 x 8.05 x 10-7 v22   - 0]

solving we get v2 = 380.75m/s

2) Magnetic field

required magnetic force , Fm = q v2 B = 9.242 x 10-6 N

radius of curvature, r = mv2 / (q B) = 12627.04 meters = 12.67 km

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