Charged particles are accelerated through a potential V and then pass between two charged plates, separated by a distance d and with a potential Ve between them. In the region between the plates, a uniform magnetic field B is tuned so that the particles are not deflected. Suppose now that the magnitude of B is increased by a factor of 4. By what factor must V be changed so that the particles are still not deflected? 6.AO 16 BO 1 CO 1/4 DO 1/16 EO 4 2
Solution
work done by potential difference V1 = V1*q
kinetic energy of particel K = (1/2)*m*v^2
work energy relation
K = W
(1/2)*m*v^2 = V1*q
speed v = sqrt(2*V1*q/m)
In between the plated
electric force Fe = E*q = (V2/d)*q
magnetic force Fb = q*v*B = q*sqrt(2*V1*q/m)*B
for no delfection
Fb = Fe
q*sqrt(2*V1*q/m)*B = (V2/d)*q
sqrt(2*V1*q/m)*B = (V2/d)
(2*V1*q/m)*B^2 = (V2/d)^2
V1 = V2^2*m/(2*q*B^2*d^2)
V1/V1\' = (B\'/B)^2
B\' = B/4
V1\' = ?
V1/V1\' = 1/16
V1\' = V1*16
V1 is increased by a factor of 16 <<<----------ANSWER
OPTION ( A )
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Charged particles are accelerated through a potential V and then pass.docx
1. Charged particles are accelerated through a potential V and then pass between two charged
plates, separated by a distance d and with a potential Ve between them. In the region between the
plates, a uniform magnetic field B is tuned so that the particles are not deflected. Suppose now
that the magnitude of B is increased by a factor of 4. By what factor must V be changed so that
the particles are still not deflected? 6.AO 16 BO 1 CO 1/4 DO 1/16 EO 4 2
Solution
work done by potential difference V1 = V1*q
kinetic energy of particel K = (1/2)*m*v^2
work energy relation
K = W
(1/2)*m*v^2 = V1*q
speed v = sqrt(2*V1*q/m)
In between the plated
electric force Fe = E*q = (V2/d)*q
magnetic force Fb = q*v*B = q*sqrt(2*V1*q/m)*B
for no delfection
Fb = Fe
2. q*sqrt(2*V1*q/m)*B = (V2/d)*q
sqrt(2*V1*q/m)*B = (V2/d)
(2*V1*q/m)*B^2 = (V2/d)^2
V1 = V2^2*m/(2*q*B^2*d^2)
V1/V1' = (B'/B)^2
B' = B/4
V1' = ?
V1/V1' = 1/16
V1' = V1*16
V1 is increased by a factor of 16 <<<----------ANSWER
OPTION ( A )
