A few electric field lines for a system of two charges $Q_{1}$ and $Q_{2}$ fixed at two different points on the x-axis are shown in the figure. These lines suggest that

(This question has multiple correct options)
$A . | Q_{1} | > | Q_{2} |$
$B . | Q_{1} | < | Q_{2} |$
C. at a finite distance to the left of $Q_{1}$ , the electric field is zero
D. at a finite distance to the right of $Q_{2}$ , the electric field is zero

Question

A few electric field lines for a system of two charges ${{Q}_{1}}$ and ${{Q}_{2}}$ fixed at two different points on the x-axis are shown in the figure. These lines suggest that

(This question has multiple correct options)$\text{A}\text{.  }\left| {{Q}_{1}} \right|>\left| {{Q}_{2}} \right|$$\text{B}\text{.  }\left| {{Q}_{1}} \right|<\left| {{Q}_{2}} \right|$C.    at a finite distance to the left of ${{Q}_{1}}$, the electric field is zeroD.    at a finite distance to the right of ${{Q}_{2}}$, the electric field is zero

Vedantu Content Team · Accepted Answer

Hint: The charge with greater magnitude produces greater magnitude of electric field. This is depicted by drawing more number of field lines near the charge of greater magnitude. A positive point charge produces an electric field at a point that is directed radially outwards. A negative point charge produces an electric field at a point that is directed radially inwards.

Complete answer:
A positive point charge produces electric field lines that are directed radially outwards.
A negative point charge produces electric field lines that are directed radially inwards.
Therefore, in a system of one positive charge and negative charge, the electric field lines originate from the positive charge and they end at the negative charge.
In the given figure, we can see that the electric field lines are emerging from the charge

Q_{1}

and they are ending at the charge

Q_{2}

.
Hence, the charge

Q_{1}

is a positive charge and the charge

Q_{2}

is negative charge.
The charge with greater magnitude produces a greater magnitude of electric field. This is depicted by drawing more number of field lines near the charge of greater magnitude.
Therefore, the magnitude of charge

Q_{1}

is greater than the magnitude of charge

Q_{2}

.
i.e.

| Q_{1} | > | Q_{2} |

.
Therefore, option A is correct.
If we consider a point on the x-axis to the left of charge

Q_{1}

, then the electric field due to charge

Q_{1}

is directed towards left and the electric field due to the charge

Q_{2}

is directed towards right.

Therefore, there will be a point to the left of the charge where the two electric fields will cancel out each other and the net electric field is zero.
Similarly, there will be a point at finite distance to the right of charge

Q_{2}

where the net electric field is zero.
Therefore, the options C and D are correct.

Hence, the correct options are A, C and D.

Note:
We can also note one more point that in the region that has greater magnitude of electric field, the field lines are closer than the region with smaller magnitude of electric field.
We can see that the field lines are closer near the charge

Q_{1}

and the fields are more spaced near the charge

Q_{2}

. Hence,

| Q_{1} | > | Q_{2} |

.

Therefore, there will be a point to the left of the charge where the two electric fields will cancel out each other and the net electric field is zero.Similarly, there will be a point at finite distance to the right of charge ${{Q}_{2}}$ where the net electric field is zero.Therefore, the options C and D are correct.Hence, the correct options are A, C and D.   Note: We can also note one more point that in the region that has greater magnitude of electric field, the field lines are closer than the region with smaller magnitude of electric field.We can see that the field lines are closer near the charge ${{Q}_{1}}$ and the fields are more spaced near the charge ${{Q}_{2}}$. Hence, $\left| {{Q}_{1}} \right|>\left| {{Q}_{2}} \right|$.

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