Tag: physics

Questions Related to physics

The linear charge density of a thin metallic rod varies with the distance $'x'$ from one end as $\lambda  = {\lambda _0}{x^2}\left( {0 \leqslant x \leqslant l} \right).$ The total charge on the rod is:

physics static electricity exchange of electrons methods used for charging electric charge

  1. $\dfrac{{{\lambda _0}{l^3}}}{3}$

  2. $\dfrac{{{\lambda _0}{l^4}}}{3}$

  3. $\dfrac{{2{\lambda _0}{l^3}}}{3}$

  4. $\dfrac{{{\lambda _0}{l}}}{2}$

Show answer
Correct Option: D
Explanation:
$\lambda =\dfrac {\lambda _0 x}{L}$
$Q=\displaystyle \int _0^L \lambda \ dx$
$=\displaystyle \int _0^L \dfrac {\lambda _0 x}{L}dx$
$=\dfrac {\lambda _0}{L} \dfrac {x^2}{2}\displaystyle \int _0^L$
$=\dfrac {\lambda _0}{L}\times \dfrac {L^2}{2}$
$=\dfrac {\lambda _0L}{2}$

A hollow metal sphere, Sphere A, sits on an insulating stand. Sphere A has a diameter of 4 inches, and a net charge of magnitude $Q _0$. A second hollow metal sphere, Sphere B, also sits on an insulating stand, but has a diameter of 8 inches and zero net charge. The two spheres are brought close so that they touch, then they are separated.
In terms of $Q _0$, what is the final charge on Sphere A?

physics static electricity exchange of electrons methods used for charging electric charge

  1. $\cfrac{Q _0}{5}$

  2. $\cfrac{Q _0}{4}$

  3. $\cfrac{Q _0}{2}$

  4. $Q _0$

  5. $4Q _0$

Show answer
Correct Option: A
Explanation:

$R _B=2R _A$


Let final charge on spheres be $Q _A$ and $Q _B$.

On touching the spheres charge density becomes same.

And, charge density, $\sigma=\dfrac{Q}{4\pi R^2}$

$\implies Q\propto R^2$ for same $\sigma$

Hence, $\dfrac{Q _B}{Q _A}=\dfrac{R _B^2}{R _A^2}=2^2$

$\implies Q _B=4Q _A$

And, total charge$=Q _B+Q _A=Q _o$

$\implies 4Q _A+Q _A=Q _o$

$\implies Q _A=\dfrac{Q _o}{5}$

Answer-(A)

State whether true or false :
Magnetization by electric current method creates more powerful magnets than other  methods of magnetization.

physics properties of a magnetic field let's make a magnet making magnets making and handling magnets

  1. True

  2. False

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Correct Option: A
Explanation:

Magnetization. There are a variety of methods that can be used to establish a magnetic field in a component for evaluation using magnetic particle inspection. It is common to classify the magnetizing methods as either direct or indirect. With direct magnetization, current is passed directly through the component.Rubbing the nail with the permanent magnet causes a stronger, more lasting magnetism in the nail. For this to work, only one pole of the magnet must stroke the nail from one end to the other in a single direction. ... It usually takes around 20 to 30 strokes before the nail becomes sufficiently magnetized.

For a permanent magnet, properties of material should be

physics properties of a magnetic field let's make a magnet making magnets making and handling magnets

  1. high retentivity high coercivity

  2. low retentivity law coercivity

  3. high retentivity low coercivity

  4. low retentivity high coercivity

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Correct Option: A

A rod of cross-sectional area $10$ $cm^2$ is placed with its length parallel to a magnetic field of intensity $1000$ ${A/m}$ , the flux through the rod is $10^4$ $webers$. Then the permeability of material of the rod is:

physics properties of a magnetic field let's make a magnet making magnets making and handling magnets

  1. $10^4$ ${wb/Am}$

  2. $10^3$ ${wb/Am}$

  3. $10^2$ ${wb/Am}$

  4. $10$ ${wb/Am}$

Show answer
Correct Option: A
Explanation:
Magnetic field of intensity $(H)=1000\ A/m$
$Flux$ through rod $(\phi)=10^4 \ Wb$
Area of mass section $(A)=10\ cm^2 =10\times 10^{-4}m^2$
$\Rightarrow \ A=10^{-3}m^2$

we know,
$\boxed {B=\dfrac {\phi}{A}= \mu H}$           (where $B$ is magnetic flux density)
  $\Rightarrow \ \dfrac {10^4}{10^{-3}}= \mu (1000)$
$\ \Rightarrow \ \mu =\dfrac {10^4}{10^{-3} \times 1000}=10^4\ Wb /Am$

hence $\boxed {\mu =10^4 \ Wb/Am}$,

so $(A)$ option is correct

permeability of material of rod

A domain in a ferromagnetic substance is in form of a cube of side length $1 \,\mu m$. It is contains $8 \times 10^{10}$ atoms and each atomic dipole has a moment of $9 \times 10^{-24} A \,m^2$, then the magnetization of the domain is then

physics properties of a magnetic field let's make a magnet making magnets making and handling magnets

  1. $7.2 \times 10^5 \,A \,m^{-1}$

  2. $7.2 \times 10^3 \,A \,m^{-1}$

  3. $7.2 \times 10^9 \,A \,m^{-1}$

  4. $7.2 \times 10^{12} \,A \,m^{-1}$

Show answer
Correct Option: A
Explanation:

Magnitisation $= \dfrac{M}{v}$

$= \dfrac{8 \times 10^{10} \times 9 \times 10^{-24}}{(10 - 6)^3}$

$= 7.2 \times 10^5 \,Am^{-1}$

The magnetic force required to demagnetize the material is called:

physics properties of a magnetic field let's make a magnet making magnets making and handling magnets

  1. Retentivity

  2. Coercivity

  3. Energy loss

  4. Hysteresis

Show answer
Correct Option: B
Explanation:

The coercivity of a substance is a measure of the reverse magnetising field required to destroy the residual magnetism of the substance.

A permanent magnet in the shape of a thin cylinder of length $10$cm has magnetisation $(M) = 10^6 A m^{-1}$. It's magnetization current $I _M$ will be then

physics properties of a magnetic field let's make a magnet making magnets making and handling magnets

  1. $10^5$A

  2. $10^6$A

  3. $10^7$A

  4. $10^8$A

Show answer
Correct Option: A
Explanation:

Given,

$M=10^6 A/m$
$l=10cm=0.1m$
Magnetization, $M=\dfrac{I _M}{l}$ 
$I _M=Ml=10^6\times 0.1$
$I _M=10^5A$
The correct option is A.

The marked end of a compass needle always points directly to

magnetic compass magnetic poles and magnetic compass properties of magnet effect of electric current physics

  1. Earth's geographic South Pole

  2. Earth's geographic North Pole

  3. A magnet's south pole

  4. A magnet's north pole

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Correct Option: C
Explanation:

The marked end of compass needle always points to the south pole of a magnet.

The geographic north pole of the earth is the magnetic south pole. 
Hence it points towards the geographic north pole of earth.

The tangent law is applicable only when

magnetic compass magnetic poles and magnetic compass properties of magnet effect of electric current physics

  1. There are atleast two magnetic field

  2. There are two uniform magnetic fields mutually perpendicular to each other

  3. One strong magnetic field and the other weak magnetic field

  4. In the present magnetic fields one should be horizontal component of the earth's magnetic field

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Correct Option: B