Q.49. A three coulomb charge moves from the point (0, -2, -5) to the point (5, 1, 2) in an electric

Q: What is the correct answer for JEE Main Physics Q49?

The correct answer is 186. The work done by an electric field on a charge $q$ moving from point A to point B is $W = -q \Delta V = -q (V_B - V_A)$. Alternatively, $W = \int_A^B \vec{F} \cdot d\vec{l} = \int_A^B q\vec{E} \cdot d\vec{l}$. Given $q = 3$ C. $\vec{E} = 2x\hat{i} + 3y^2\hat{j} + 4\hat{k}$. $d\vec{l} = dx\hat{i} + dy\hat{j} + dz\hat{k}$. So, $W = q \int_{(0,-2,-5)}^{(5,1,2)} (2x dx + 3y^2 dy + 4 dz)$. $W = 3 \left

Q: Q.49. A three coulomb charge moves from the point (0, -2, -5) to the point (5, 1, 2) in an electric field expressed as N/C. The work done in moving the charge is ________ J.

The correct answer is 186. The work done by an electric field on a charge $q$ moving from point A to point B is $W = -q \Delta V = -q (V_B - V_A)$. Alternatively, $W = \int_A^B \vec{F} \cdot d\vec{l} = \int_A^B q\vec{E} \cdot d\vec{l}$. Given $q = 3$ C. $\vec{E} = 2x\hat{i} + 3y^2\hat{j} + 4\hat{k}$. $d\vec{l} = dx\hat{i} + dy\hat{j} + dz\hat{k}$. So, $W = q \int_{(0,-2,-5)}^{(5,1,2)} (2x dx + 3y^2 dy + 4 dz)$. $W = 3 \left

Question

Q.49. A three coulomb charge moves from the point (0, -2, -5) to the point (5, 1, 2) in an electric field expressed as  N/C. The work done in moving the charge is ________ J.

FirstInTest · Accepted Answer

The work done by an electric field on a charge $q$ moving from point A to point B is $W = -q \Delta V = -q (V_B - V_A)$. Alternatively, $W = \int_A^B \vec{F} \cdot d\vec{l} = \int_A^B q\vec{E} \cdot d\vec{l}$. Given $q = 3$ C. $\vec{E} = 2x\hat{i} + 3y^2\hat{j} + 4\hat{k}$. $d\vec{l} = dx\hat{i} + dy\hat{j} + dz\hat{k}$. So, $W = q \int_{(0,-2,-5)}^{(5,1,2)} (2x dx + 3y^2 dy + 4 dz)$. $W = 3 \left[ \int_0^5 2x dx + \int_{-2}^1 3y^2 dy + \int_{-5}^2 4 dz ight]$. $W = 3 \left[ [x^2]_0^5 + [y^3]_{-2}^1 + [4z]_{-5}^2 ight]$. $W = 3 \left[ (5^2 - 0^2) + (1^3 - (-2)^3) + (4 	imes 2 - 4 	imes (-5)) ight]$. $W = 3 \left[ (25) + (1 - (-8)) + (8 - (-20)) ight]$. $W = 3 \left[ 25 + 9 + 28 ight]$. $W = 3 \left[ 62 ight] = 186$ J.

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