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Question

The magnetic field in the figure is decreasing at the rate 0.8 T/s . What is the magnitude of the acceleration of a proton at rest at point c and d?

Answer “What is the magnitude of the acceleration of a proton at rest at point c and d?”.

Induced electric field:

A conductor is affected by magnetic flux. The induced electric field can change in time and is therefore not conservative.

Mathematically:

Here;

• $E$ is the electric field,

• $l$ is the line element around the electric field,

• ${\varphi }_m$ is the magnetic flux

• $t$ is the time.

Answer and Explanation:

We only need to consider the magnitude in Faraday’s law:

For a uniform electric field;

Here,

•  is the radius of the circle

Since the magnetic field is perpendicular to the area of the circle, magnetic flux;

${\varphi }_{\mathrm{m\; =\; 2\pi rB}}$

Here,

• $B$ is the magnetic field.

Therefore, from eqn.(1), we get;

The force on a proton at distance (r) from the center is now;

F = qE = ma

a =

Here,

• $q=1.6\times \text{C}$ is the charge of the proton,

• $m=1.67\times \text{kg}$ is the mass of the proton.

Thus,

a =

At point c, $r=1\text{cm}=0.01\text{m}$

a =

=

At point d, $r=2\text{cm}=0.02\text{m}$

a =

=

Last words

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