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Byju's Answer

Standard XII

Physics

The Circular Motion

A particle of...

Question

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

E = \frac{3 m v^{2}}{4 q a}

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Rate of work done by electric field at P is

\frac{3 m v^{3}}{4 a}

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Rate of work done by electric field at P is zero.

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Rate of work done by both the fields at Q is zero.

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Solution

The correct options are
A $E = \frac{3 m v^{2}}{4 q a}$
B Rate of work done by electric field at P is $\frac{3 m v^{3}}{4 a}$
D Rate of work done by both the fields at Q is zero.
In going from P to Q increase in kinetic energy
$\frac{1}{2} m (2 V)^{2} - \frac{1}{2} m V^{2} = \frac{1}{2} m (3 V^{2}) =$ Work done by electric field
or, $\frac{3}{2} m v^{2} = E q \times 2 a \Rightarrow E = \frac{3 m v^{2}}{4 q a}$
The rate of work done by E at $P = f o r c e d u e t o E \times v e l o c i t y .$
$= q E v = q (\frac{3 m v^{2}}{4 q a}) v = \frac{3 m v^{3}}{4 a}$
At q, $\to v$ is perpendicular to $\to E$ and $\to B$ , therefore no work done by the either field. Hence (A), (B) & (D) are correct.

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Similar questions

Q. A particle of charge +q and mass m moving under the influence of a uniform electric field

E^i

and a uniform magnetic field

B^k

follows trajectory from P to Q as shown in figure. The velocities at P and Q are

v^i

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- 2 v^j

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Q. A charged particle of mass

m

and charge

q

, moving under the influence of a uniform electric field

E^i

and a uniform magnetic field

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, follows a trajectory from point

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Q

as shown in figure. The velocities at

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are respectively,

v^i and - 2 v^j

. Then, which of the following statements (A, B, C, D) are correct? (Trajectory shown is schematic and not to scale)

(A)

E = \frac{3}{4} (\frac{m v^{2}}{q a})

(B)

Rate of work done by the electric field at

P

\frac{3}{4} (\frac{m v^{2}}{a})

(C)

Rate of work done by both the fields at

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(D)

The difference between the magnitude of angular momentum of the particle at

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2 m a v

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Q (2 a, a)

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v^i

and at

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2 v^i

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Q. Point charge q moves from point P to point S along the path PQRS (figure shown) in a uniform electric field E pointing coparallel to the positive direction of the axis. The coordinates of the points and are and respectively. The work done by the field in the above process is given by the expression

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A particle of charge +q and mass m moving under the influence of a uniform electric field E^i and a uniform magnetic field B^k follows trajectory from P to Q as shown in figure. The velocities at P and Q are V^i and −2V^j respectively. Which of the following statement(s) is/are correct?

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