Electric Potential Due to Infinite Line of Charge

Q.

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नीचे दिये गये प्रश्न के लिए अनुच्छेद

An electric dipole is a system consisting of two charges of equal magnitudes but opposite signs, separated by a certain distance. Dipole moment is defined as the product of magnitude of either charge and distance between the two charges and has direction from negative to positive charge. Consider the following charge arrangement.

एक विद्युत द्विध्रुव ऐसा निकाय है जिसमें समान परिमाण लेकिन विपरीत चिन्हों वाले दो आवेश एक निश्चित दूरी द्वारा पृथक्कृत है। द्विध्रुव आघूर्ण को किसी एक आवेश के परिमाण तथा दोनों आवेशों के मध्य दूरी के गुणन के रूप में परिभाषित किया जाता है तथा इसकी दिशा ऋणात्मक से धनात्मक आवेश की ओर होती है। निम्नलिखित आवेश समंजन पर विचार कीजिए।

Q. The magnitude of net electric dipole moment of the system is

प्रश्न - निकाय के नेट विद्युत द्विध्रुव आघूर्ण का परिमाण है

1. $8\sqrt{2}$ C m
2. 8 C m
3. $2\sqrt{7}$ C m
4. $9\sqrt{2}$ C m

Q. Find the work done by external agent in moving a $1C$ charge from point P to Q in presence of an infinitely long uniformly charged line of linear charge density $\lambda$ as shown.

1. $\frac{\lambda }{2\pi {\epsilon }_0}\ln 1.5$
2. $\frac{\lambda }{2\pi {\epsilon }_0}$
3. $\frac{\lambda }{2\pi {\epsilon }_0}\ln 5$
4. $\frac{7\lambda }{2\pi {\epsilon }_0}$

Q. Determine the electric field strength vector if the potential of this field depends on $x,y$ coordinates as $V=10axy$.

1. $10a(y\hat{i}+x\hat{j})$
2. $-10a(y\hat{i}+x\hat{j})$
3. $-10a(x\hat{j}+y\hat{k})$
4. $-a(y\hat{i}+x\hat{j})$

Q. Two identical thin rings, each of radius $R$, are coaxially placed a distance $R$ apart . If $Q_1$ and $Q_2$ are respectively the charges uniformly spread on the two rings, the work done in moving a charge $q$ from the centre of one ring to that of the other is equal to

1. $\frac{q(Q_1-Q_2)(\sqrt{2}+1)}{\sqrt{2}\left(4\pi {\epsilon }_{0}R\right)}$
2. $\frac{q(Q_1-Q_2)(\sqrt{2}-1)}{\sqrt{2}\left(4\pi {\epsilon }_{0}R\right)}$
3. Zero
4. $\frac{q(Q_1+Q_2)(\sqrt{2}-1)}{\sqrt{2}\left(4\pi {\epsilon }_{0}R\right)}$

Q. The figure shows a non-conducting ring with positive and negative charge non uniformly distributed on it such that the total charge is zero. Which of the following statements is true?

1. The potential at all the points on the axis will be zero.
2. The electric field at all the points on the axis will be zero.
3. The direction of the electric field at all points on the axis will be along the axis
4. If the ring is placed inside a uniform external electric field, then net torque and force acting on the ring would be zero.