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A particle of charge +q and mass m movi...

A particle of charge ` +q` and mass `m` moving under the influence of a uniform electric field ` E hat(i)` and uniform magnetic field ` B hat(k)` follows a trajectory from ` P to Q` as shown in fig. The velocities at `P and Q` are ` v hat(i)` and ` - 2v hat(j)` . which of the following statement(s) is/are correct ?

A

` E = (3)/(4) [ (mv^(2))/(qa)]`

B

Rate of work done by the electric field at `P` is ` 3/4[ (mv^(3))/(a)]`

C

Rate of work done by the electric field at `p` is zero

D

Rate of work done by the electric field at `Q` is zero

Text Solution

Verified by Experts

The correct Answer is:
A, B, D
Considering the activity from `P to Q` ( Horizontal)
` u_(1) = v, v_(1) = 2v, s_(1) = 2a , Acc = A`
rArr ` 4v^(2)- v^(2) = 2A(2a)`
rArr `A = (3v^(2))/(4a)`
Force acting in the horizontal direction is
` F = q ^(E) = mA`
rArr `E = (mA)/(q) = 3/4[ (mv^(2))/(qa)]`
Rate of doing work A `P`
power ` = Fxxv = mAxxv = 3/4[(mv^(3)/(a)]`
Rate of doing work by the magnetic field is throughout zero. The rate of doing work by eletric field is zero at `Q` . Because at `Q` , the angle between force due to electric field and displacement is zero .

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